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Cities in Bad Shape: Urban Geometry in India�
Maria�avia Harariy
MIT
This version: 15 October 2014.Preliminary and incomplete. Please do not cite or circulate.
Abstract
The spatial layout of cities is an important determinant of urban commuting e¢ ciency.
This paper investigates the economic implications of urban geometry in the context of
India. A satellite-derived dataset of night-time lights is combined with historic maps to
retrieve the geometric properties of urban footprints in India over time. My approach
relies on a novel city-year level instrument for urban shape, which combines geography
with a mechanical model for city expansion. I investigate how city shape a¤ects the
location choices of consumers, in a spatial equilibrium framework à la Roback-Rosen.
Cities with more compact shapes are characterized by larger population, lower wages, and
higher housing rents, consistent with compact shape being a consumption amenity. The
implied welfare cost of deteriorating city shape is estimated to be sizeable. I also attempt
to shed light on policy responses to deteriorating shape. The adverse e¤ects of unfavorable
topography appear to be exacerbated by building height restrictions, and mitigated by
road infrastructure.
�I am grateful to my advisers Esther Du�o, Ben Olken and Dave Donaldson for their invaluable help
throughout this project. I also thank Alex Bartik, Jie Bai, Nathaniel Baum-Snow, Alain Bertaud, Melissa
Dell, John Firth, Ludovica Gazzè, Michael Greenstone, Gabriel Kreindler, Matthew Lowe, Rachael Meager,
Yuhei Miyauchi, Hoai-Luu Nguyen, Paul Novosad, Arianna Ornaghi, Bimal Patel, Champaka Rajagopal, Otis
Ried, Adam Sacarny, Albert Saiz, Ashish Shenoy, Chris Small, Kala Sridhar, William Wheaton and participants
to the MIT Development Lunch, Applied Micro Lunch and Development Seminar for helpful comments and
discussions at various stages of this [email protected]
1
1 Introduction
Most urban economics assumes implicitly that cities are circular or star-shaped. Real-world
cities, however, often depart signi�cantly from this assumption: cities display considerable
variation in shape. Urban geometries are jointly determined by a combination of geography and
policy (Bertaud, 2004). On the one hand, existing natural and topographic constraints prevent
cities from expanding radially in all directions. On the other, regulation and infrastructural
investment can a¤ect urban expansion both directly and indirectly. For instance, master plans
can explicitly promote polycentricity, by planning satellite centers around existing ones. Land
use regulations can encourage land consolidation, resulting in a more compact, as opposed
to fragmented development pattern. Investments in road infrastructure can encourage urban
growth along transport corridors.
While the economics literature has devoted very little attention to the geometry of cities,
in �elds such as urban planning and transportation engineering city shape is considered an
important determinant of commuting e¢ ciency, more compact shapes being characterized by
shorter trips and more cost-e¤ective transport networks. This, in turn, is claimed to a¤ect
productivity and welfare. Emphasizing the role of city shape in the functioning of public and
private transport, Bertaud (2004) argues that contiguous and compact urban development can
improve the welfare of city dwellers, by providing better and cheaper access to most of the
jobs. This is thought to be particularly relevant in the megacities of the developing world,
where most inhabitants cannot a¤ord individual means of transportation or where the large
size of the city precludes walking as a mean of getting to jobs. Cervero (2002) emphasizes
how compact, accessible cities are potentially more productive, through a combination of labor
market pooling, savings in transporting inputs and technological and information spillovers.
This urban planning literature is mostly descriptive
In this paper I investigate empirically the economic implications of city shape in the context
of India. More speci�cally, I examine two complementary sets of questions: �rst, how city
geometry a¤ects the location choices of consumers, in the framework of spatial equilibrium
across cities, and what the welfare implications of deteriorating city shape are. Second, how
policy interacts with geography in determining urban form.
India represents a promising setting to study urban spatial structures for a number of reasons.
First, as most developing countries, India is experiencing fast urban growth. According to the
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2011 Census, the urban population amounts to 377 million, increasing from 285 million in 2001
and 217 million in 1991, representing between 25 and 31 percent of the total. Although the pace
of urbanization is slower than in other Asian countries, it is accelerating, and it is predicted
that another 250 million will join the urban ranks by 2030 (Mc Kinsey, 2010). This growth
in population has been accompanied by a signi�cant physical expansion of urban footprints,
typically beyond urban administrative boundaries (Indian Institute of Human Settlements,
2013; World Bank, 2013). This setting thus provides a unique opportunity to observe the
shapes of cities as they evolve and expand over time. Such an exercise would not be feasible
in a developed context: urban spatial structures in developed countries are typically very
resilient and path dependent (Bertaud, 2004), which would prevent me from detecting signi�cant
variation over time.
Secondly, India is characterized by a di¤used urbanization pattern. With an unusually large
number of highly-populated cities, India contrasts from other developing countries characterized
by the presence of a large capital city and very few other urban centers. This ensures a large
enough sample of cities for the econometric analyses which I carry out.
Moreover, the challenges posed by urban expansion have been gaining increasing importance
in India�s policy discourse, which makes it particularly relevant to investigate these matters from
an economics perspective. On the one hand, this debate has focused on the perceived harms of
haphazardous urban expansion, most notably limited urban mobility and lengthy commutes.
According to a recent Mc Kinsey report (2010), the average peak morning commute in Indian
million-plus cities is in excess of one-and-a-half to two hours. Providing e¤ective urban public
transit systems has been consistently identi�ed as a key policy recommendation for the near
future (e.g. Mitric and Chatterton, 2005; World Bank, 2013; Mc Kinsey, 2013.). On the other
hand, there is a growing concern that existing policies �in particular, urban land use regulations
�might directly or indirectly contribute to distorting urban form (World Bank, 2013, Sridhar,
2010, Glaeser, 2011). The most paradigmatic of these measures are restrictions on building
height, in the form of Floor Area Ratios (FARs). FARs in Indian cities are considered very
restrictive compared to international standards, and have been indicated as one of the causes of
sprawl in Indian cities (Brueckner and Sridhar, 2012; Bertaud and Brueckner, 2005). Another
example is given by the Urban Land Ceiling and Regulation Act, which has been claimed to
hinder intra-urban land consolidation and restrict the supply of land available for development
within cities (Sridhar, 2010).
3
My broad research question concerns the economic implications of city shape. In particular,
in this project I am interested in two complementary sets of issues. The �rst and main question
relates to how city shape a¤ects the location choices of consumers across cities. I investigate this
in the framework of a model of spatial equilibrium across cities à la Roback-Rosen, modelling
city shape as an amenity. My �ndings are broadly consistent with "good city shape" being a
consumption amenity. I �nd robust evidence that cities with more compact shapes grow faster,
all else being equal. There is also some evidence that consumers are paying a premium in terms
of lower wages and higher rents in order to live in cities with better geometries. I estimate the
implied welfare cost of deteriorating shape, �nding that it is sizeable and considerably larger
than the mere monetary cost associated to lengthier commutes.
A natural question which arises next concerns the role of policy: if city shape indeed has
welfare implications, what is the optimal policy response to existing topographic constraints?
Although a thorough investigation of this question might require more detailed data than those
used in this study, in the concluding part of this paper I make a preliminary attempt to explore
the interactions between topography, regulation and city shape. I �nd that restrictions on
building height - in the form of low FARs - result in cities which are more spread out in space
and less compact than their topography would predict. This is consistent with one of the
most common arguments against restrictive FARs in India, namely that they cause sprawl by
preventing cities from growing vertically (Glaeser, 2011).
My methodology can be outlined as follows. The bulk of my empirical analysis is conducted
at the city-year level and is based on an instrumental variable approach. I assemble an un-
balanced panel dataset of urban footprints for about 400 Indian cities, by combining historic
maps (1950) with a satellite-derived dataset of night-time lights (1992-2010). I compute sev-
eral geometric indicators for urban shape, used in urban planning as proxies for the patterns
of within-city trips. I develop an original instrument for city shape by combining geography
with a mechanical model for city expansion. The underlying idea is that, as cities expand in
space, they face di¤erent geographic constraints - steep terrain or water bodies - leading to
departures from an ideal circular expansion path. The construction of my instrument requires
two steps. First, I use a mechanical model for city expansion to predict the area which a city
should occupy in a given year. I consider two versions of this model: one based on each city�s
historic population growth rates, and one postulating a common growth rate for all cities. Sec-
4
ond, I consider the largest contiguous patch of developable land within this predicted radius
("potential footprint") and compute its shape properties. I then proceed to instrument the
shape properties of the actual city footprint in that given year with the shape properties of
the potential footprint. The resulting instrument varies at the city-year level, allowing me to
control for time-invariant city characteristics through city �xed e¤ects. The identi�cation of
the impact of shape thus relies on comparing geography-driven changes in urban shape over
time for each city. My main results are summarized below.
(i) I �nd a strong, robust �rst stage linking the actual shape that a city�s footprint has at a
given point in time and the potential shape which it can have given the layout of the geographic
constraints surrounding it. This is not solely driven by extremely constrained topographies (e.g.
coastal or mountainous cities) in my sample.
(ii) There is a strong and robust negative IV relationship between population and non-
compactness, conditional on area. My most conservative estimate indicates that a one standard-
deviation deterioration in city shape entails decrease in population density of 0.9 standard
deviations.
(iii) There is suggestive evidence that households are paying for compact geometry both
through higher housing prices and through lower wages. Using district level averages as proxies
for city-level data, I �nd a marginally signi�cant negative relationship between non-compactness
and rents per square meter, and a positive relationship between non-compactness and wages.
Although noisy, these results are consistent with "good shape" being valued a consumption
amenity. Using these estimates in conjunction with a simple version of the Rosen-Roback
model, I �nd that a one standard deviation deterioration in city shape entails a welfare loss
equivalent to a 5% decrease in income.
(iv) Interacting city shape with di¤erent proxies for infrastructure, I �nd that the negative
e¤ects of poor geometry on population growth are mitigated by a denser road network and by
the availability of motor vehicles, suggesting that commute times could be the main mechanism
through which city shape a¤ects consumers.
(v) Cities with poorer shapes are characterized by comparatively fewer slum dwellers and
houses of better quality. This is consistent with the interpretation that low-income immigrants
tend to sort into more compact cities, possibly because they are less able to cope with lengthy
commutes.
The �nal part of my work attempts to look at the endogenous responses to unfavorable city
5
shape. Due to data limitations, most of these results are based on a cross-section of cities only,
and should therefore be interpreted as suggestive.
(vi) Restrictive FARs result in footprints which are both larger and less compact. Higher
FARs, on the other hand, mitigate the negative e¤ects of poor geometry on population growth.
(vii) Cities with worse geometries appear to have a less dense road network in absolute terms,
but road density per capita is not signi�cantly di¤erent from that observed in more compact
cities.
(viii) Productive establishments appear less spatially concentrated in non-compact cities.
This could re�ect a tendency of cities to become less monocentric as their shape deteriorates.
This projects contributes to the existing literature in a number of directions. The �rst
concerns the analysis of urban geometry from an economics standpoint. To my knowledge,
this is the �rst work which studies city shape as an amenity. The second is methodological
and relates to the measurement of the properties of urban footprints. I employ the OLS night-
time lights dataset to track the shape of urban footprints over time, following an approach
which has been used in urban remote sensing, but not in economics. The use of shape metrics
borrowed from the urban planning literature to measure economically relevant properties of
urban footprints is also novel. Furthermore, I develop an original instrument for city shape,
which is potentially applicable to other contexts as well.
The remainder of the paper is organized as follows. Section 2 brie�y reviews the existing
literature. Section 3 outlines the conceptual framework. Section 4 documents my data sources
and describes the geometric indicators which I employ. Section 5 presents my empirical strategy
and describes in detail how my instrument is constructed. The empirical evidence is presented
in the following two Sections. Section 6 discusses my main results, which pertain to the e¤ects
of city shape on the location choices of consumers. Section 7 provides some results on other
endogenous responses to city shape, including interactions between topography and policy.
Section 8 concludes with indications for future work.
2 Previous Literature
The economics literature on urban spatial structures has mostly focused on two aspects of urban
form: city size and population density gradient. The classic monocentric city model (Alonso,
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1964; Mills, 1967, 1972; Muth, 1969) postulates the existence of a single employment center
and predicts the formation of a circular city with declining density gradient, and whose radius
declines with transportation costs. Richer polycentric city models were subsequent developed,
where the number, location and spatial extent of employment centers are determined endoge-
nously in a linear or circular city (Fujita and Ogawa, 1982, Lucas and Rossi-Hansberg, 2002).
Although these models can in principle be altered to generate non-circular cities, for instance,
assuming the road network is not radial (Brueckner, 2011, p. 56), the focus of this literature
is on the determinants of the internal structure of cities, and the implications of geometry are
left unexplored. My approach is di¤erent since I take the shape of each city as given and I
investigate its e¤ects on the spatial equilibrium across, rather than within cities.
The conceptual framework I draw upon is that on spatial equilibrium across cities, after
Rosen(1979) and Roback(1982). In the simplest version of this model, consumers and �rms
endogenously choose to locate in cities with di¤erent levels of amenities, and wages and rents
adjust to equalize utility across locations. I model "compact city shape" as an amenity, which
a¤ects consumers and �rms primarily by reducing the length of within-city trips. Although
Glaeser (2008) acknowledges that amenities presumably include also commuting times, I am
not aware of studies explicitly looking at the link between commuting, urban geometry and the
spatial equilibrium across cities. A large empirical literature has employed the classic Rosen-
Roback framework to investigate the value of amenities (e.g. Blomquist, 1988). This literature,
however, has almost exclusively focused on the US, and has not always adequately addressed
the endogeneity of amenities (Gyourko, Kahn and Tracy, 1999).
A large empirical literature investigates urban sprawl (Glaeser and Kahn, 2004; Burch�eld
et al, 2006), typically in the context of the US. Although there is not a single de�nition of
sprawl, some studies identify sprawl with non-contiguous development (Burch�eld et al, 2006),
which is somewhat related to the notion of "compactness" which I investigate. In most analyses
of sprawl, however, the focus is on decentralization and density. I focus on a di¤erent set of
spatial properties of urban footprints: conditional on the overall amount of land used, I look
at geometric properties aimed at proxying the pattern of within-city trips. My work is more
closely related to that of Bento et al (2005), who incorporate a measure of city shape in their
investigation of the link between urban form and travel demand. However, their analysis is
based on a cross-section of US cities and does not address the endogeneity of city shape.
7
The geometric indicators of city shape which I employ are borrowed from the urban planning
and landscape ecology literature (Angel and Civco, 2009; Angel et al., 2009), which is mostly
descriptive. Urban planners emphasize the link between city shape, average intra-urban trip
length and accessibility, claiming that contiguous, compact and predominantly monocentric
urban morphologies are more favorable to transit. Bertaud (2004) argues that more compact
cities are generally more favorable to the poor, since they provide better access to jobs, but at
the same time have higher land prices, which would tend to reduce their housing �oor space
consumption. Cervero (2002) emphasizes how compact, accessible cities are potentially more
productive, through a combination of labor market pooling, savings in transporting inputs and
technological and information spillovers, and shows a correlation between labor productivity
and accessibility in US cities1.
In terms of methodology, my work is related to that of Burch�eld et al. (2006), who also
employ remotely sensed data to track urban areas over time. More speci�cally, they analyze
changes in the extent of sprawl in US cities between 1992 and 1996. The data I employ comes
mostly from night-time, as opposed to day-time imagery, and covers a longer time span (1992-
2010).
Saiz (2011) also looks at geographic constraints to city expansion, by computing the amount
of developable land within 50 km radii from US city centers and relating it to the elasticity of
housing supply. I use the same notion of geographic constraints, but I employ them in a novel
way to construct a time-varying instrument for city shape.
Finally, my work is also related to a growing literature on road infrastructure and urban
growth in developing countries (Baum-Snow and Turner, 2012; Baum-Snow et al., 2013; Morten
and Oliveira, 2014, Storeygard, 2014). In particular, Morten and Oliveira (2014) also estimate
a model of spatial equilibrium across cities, and resort to an instrumental variables approach.
Di¤erently from these studies, I do not look at the impact of roads connecting cities, but instead
focus on urban geometry as a proxy for the trips within cities.
1A subset of the urban planning and evironmental literature (reviewed by Martins et al, 2012) also looks
at the environmental implications of city shape. Bertaud (2002, 2004) argues that although compact cities are
characterized by shorter trip patterns, they might not necessarily be less polluted due to potential higher density
of motor vehicles. Most empirical analyses (e.g. Clark et al. 2011) �nd that more compact and denser cities
are less polluted, but do not separately identify the e¤ect of shape and that of density.
8
3 Conceptual Framework
In this study I interpret city shape to �rst-order as a shifter of commuting costs: all else being
equal, including city size, a city with a more compact geometry is characterized by shorter
within-city trips2. It is plausible that consumers incorporate considerations on the relative
ease of commutes when evaluating the trade-o¤s associated to di¤erent locations. This might
be even more relevant in the context of India, in which most migrants to urban areas cannot
a¤ord individual means of transport. A natural starting point in thinking how city shape
a¤ects the location choices of consumers is to interpret "good geometry" as an amenity, in the
framework of a model of spatial equilibrium à la the Rosen-Roback (Rosen 1979, Roback, 1982).
The basic underlying idea of the Rosen-Roback model is that consumers and �rms must be
indi¤erent across cities, and wages and rents allocate people and �rms to cities with di¤erent
levels of amenities. The notion of spatial equilibrium across cities presumes that consumers
are choosing across a number of di¤erent locations. The pattern of migration to urban areas
observed in India is compatible with this element of choice: according to the 2001 Census, about
38 percent of internal migrants move to a location outside their district of origin, supporting
the interpretation that they are e¤ectively choosing a city rather than simply moving to the
closest available urban location.
I draw upon the Roback model in its simplest form (Roback, 1982), following the exposition
of the model by Glaeser (2008). Households consume a composite good C and housing H. They
supply inelastically one unit of labor receiving a city-speci�c wage W . Their utility depends on
net income, i.e. labor income minus housing costs, and on a city-speci�c bundle of consumption
amenities �. Their optimization problem reads:
maxC;H
U(C;H; �) s:t: C = W � phH (1)
where ph is the rental price of housing and
U(C;H; �) = �C1��H�: (2)
In equilibrium, indirect utility V must be equalized across cities, otherwise workers would move:
V (W � phH; �) = � (3)
2In Section 4.2 I illustrate the geometric indicators I employ to measure compactness, which are all based on
the relative distances between points within a footprint. In Section 8 I discuss brie�y other possible second-order
channels through whih city shape might a¤ect consumers.
9
which given the functional form assumptions yields the condition
log(W )� � log(ph) + log(�) = V : (4)
The intuition for this condition is that consumers pay for amenities through lower wages (W )
or through higher housing prices (ph). The extent to which wages net of housing costs rise
with an amenity is a measure of the extent to which that amenity decreases utility, relative to
the marginal utility of income. Di¤erentiating this expression with respect to some exogenous
variable S - which could be (instrumented) city geometry - yields:
@ log(�)
@S= �
@ log(ph)
@S� @ log(W )
@S: (5)
This equation provides a way to evaluate the amenity value of S: the overall impact of S on
utility can be found as the di¤erence between the impact of S on housing prices, multiplied by
the share of housing in consumption, and the impact of S on wages.
Firms in the production sector also choose optimally in which city to locate. Each city is a
competitive economy that produces a single internationally traded good Y using labor N and a
local production amenity A. Their technology also requires traded capital K and a �xed supply
of non-traded capital Z. Firms solve the following production maximization problem:
maxN;K
�Y (N;K;Z;A)�WN �K
(6)
where
Y (N;K;Z;A) = AN�K Z1���
: (7)
In equilibrium �rms earn zero expected pro�ts, which are equalized across cities. Under these
functional form assumptions, the maximization problem for �rms yields the following labor
demand condition:
(1� ) log(W ) = (1� � � )(log(Z)� log(N)) + log(A) + �1: (8)
To close the model we need to specify the construction sector. Developers produce housing H
using land l and "building height" h. In each location there is a �xed supply of land L, as a
result of land use regulations3. Denoting with pl the price of land, their maximization problem
3In this framework, the amount of land to be developed is assumed to be given in the short run. It can be
argued that in reality it is an endogenous outcome of factors such as quality of regulation, success of the city
and geographic constraints. In my empirical analysis, city area will be speci�ed as a mechanical function of
predicted population growth, thus abstracting from these issues (see Section 5.2, Speci�cation I).
10
reads:
maxHfphH � C(H)g (9)
where
H = l � h (10)
C(H) = c0h�l � pll , � > 1: (11)
The construction sector operates optimally, with construction pro�ts equalized across cities.
By combining the housing supply equation resulting from the maximization problem of devel-
opers with the housing demand equation resulting from the consumers�problem, we obtain the
following housing market equilibrium condition:
(� � 1) log(H) = log(ph)� log(c0�)� (� � 1) log(N) + (� � 1) log(L) (12)
Using the three optimality conditions for consumers (4), �rms (8) and (12) this model can be
solved for the three unknowns N , W and ph , representing respectively population, wages and
housing prices, as functions of the model parameters and in particular as functions of the city
speci�c productivity parameter and consumption amenities. Denoting all constants with K,
this yields the following:
log(N) =(�(1� �) + �) log(A) + (1� )
�� log(�) + �(� � 1) log(L)
��(1� � � ) + ��(� � 1) +KN (13)
log(W ) =(� � 1)� log(A)� (1� � � )
�� log(�) + �(� � 1) log(L)
��(1� � � ) + ��(� � 1) +KW (14)
log(ph) =(� � 1)
�log(A) + � log(�)� (1� � � ) log(L)
��(1� � � ) + ��(� � 1) +KP : (15)
These conditions translate into the following predictions:
d log(N)
d log(A)> 0;
d log(N)
d log(�)> 0;
d log(N)
d log(L)> 0 (16)
d log(W )
d log(A)> 0;
d log(W )
d log(�)< 0;
d log(W )
d log(L)< 0 (17)
d log(ph)
d log(A)> 0;
d log(ph)
d log(�)> 0;
d log(ph)
d log(L)< 0: (18)
Population, wages and rents are all increasing functions of the city-speci�c productivity para-
meter. Population and rents are increasing in the amenity parameter as well, whereas wages
11
are decreasing in it. The intuition is that �rms and consumers have potentially con�icting
location preferences: �rms prefer cities with higher production amenities, whereas consumers
prefer cities with higher consumption amenities. Factor prices �W and pH �are striking the
balance between these con�icting preferences.
Consider now an indicator of urban geometry S, higher values of S denoting "worse" shapes,
in the sense of shapes conducive to longer commute trips. Assume "non-compact shape" is
purely a consumption disamenity, which decreases consumers�utility all else being equal but
does not directly a¤ect �rms�productivity:
@�
@S< 0;
@A
@S= 0 (19)
In this case we should observe the following reduced-form relationships:
dN
dS< 0;
dW
dS> 0;
dphdS
< 0 (20)
This framework predicts that a city with poorer shape should have ceteris paribus a smaller
population, higher wages and lower house rents. The intuition is that consumers prefer to
live in cities with good shapes, which drives rents up and bids wages down in these locations.
Suppose instead that poor city geometry is both a consumption and a production disamenity,
i.e. it depresses both the utility of consumers and the productivity of �rms:
@�
@S< 0;
@A
@S< 0 (21)
This would imply the following:
dN
dS< 0;
dW
dS? 0; dph
dS< 0 (22)
The model�s predictions are similar, except that the e¤ect on wages will be ambiguous. The
reason for the ambiguous sign of dWdSis that now both �rms and consumers want to locate in
compact cities. With respect to the previous case, we now have an additional force which tends
to bid wages up in compact cities: competition among �rms for locating in low-S cities. The
net e¤ect on W depends on on whether �rms or consumers value low S the most. If S is more
a consumption than it is a production disamenity, then we should observe dWdS> 0:
Assume now that
log(A) = �A + �AS (23)
log(�) = �� + ��S: (24)
12
Plugging (23) and (24) into (13),(14) and (15) we obtain:
log(N) =[(�(1� �) + �)�A + (1� )���] � S + (1� )�(� � 1) log(L)
�(1� � � ) + ��(� � 1) +KN (25)
log(W ) =[(� � 1)��A � (1� � � )���] � S � (1� � � )�(� � 1) log(L)
�(1� � � ) + ��(� � 1) +KW (26)
log(ph) =[(� � 1)�A + (� � 1)���] � S � (1� � � )(� � 1) log(L)
�(1� � � ) + ��(� � 1) +KP : (27)
For ease of exposition, de�ne:
BN =(�(1� �) + �)�A + (1� )����(1� � � ) + ��(� � 1) ; LN =
(1� )�(� � 1)�(1� � � ) + ��(� � 1) (28)
BW =(� � 1)��A � (1� � � )����(1� � � ) + ��(� � 1) ; LW =
�(1� � � )�(� � 1)�(1� � � ) + ��(� � 1) (29)
BP =(� � 1)�A + (� � 1)����(1� � � ) + ��(� � 1) ; LP =
�(1� � � )(� � 1)�(1� � � ) + ��(� � 1) : (30)
This allows us to rewrite (25); (26); (27) in a more parsimonious form:
log(N) = BNS + LN log(L) +KN (31)
log(W ) = BWS + LW log(L) +KW (32)
log(ph) = BPS + LP log(L) +KP : (33)
Note that (28); (29); (30) imply:
�A = (1� � � )BN + (1� )BW (34)
�� = �BP �BW : (35)
The welfare impact of a marginal increase in S can be quanti�ed using equation (5), which
states that in equilibrium a marginal change in log(�) needs to be compensated 1 to 1 by a
change in log(W ) :
@ log(�)
@S= �� = �
@ log(ph)
@S� @ log(W )
@S= �BP �BW : (36)
Parameter �� captures, in log points, the welfare loss form a marginal increase in S. Parameter
�A captures the impact of a marginal increase in S on city-speci�c productivity. Denote withcBN ;dBW and cBP the reduced-form estimates for the impact of S on respectively log(N); log(W )13
and log(ph):These estimates, in conjunction with plausible values for parameters �; ; �, can be
used to back out �A and ��:
c�A = (1� � � )cBN + (1� )dBW (37)b�� = �cBP �dBW : (38)
Note that this approach captures the overall, net e¤ect of S on the average city dweller, with-
out explicitly modelling the mechanism through which S enters the decisions of consumers. In
Section 6.2 I provide empirical evidence suggesting that the urban transit channel is indeed in-
volved, and in the concluding section I discuss some alternative, second-order channels through
which city shape might a¤ect consumers. This simple model also does not explicitly address
heterogeneity across consumers in tastes and skills. However, we expect that people will sort
themselves into locations based on their preferences. The estimated di¤erences in wages and
rents across cities will thus be an underestimate of true equalizing di¤erences for those with a
strong taste for the amenity of interest, and an overestimate for those with weak preferences.
The empirical evidence presented in Section 6.2 indicates that there might indeed be sorting
across cities with di¤erent geometries.
Reduced-form estimates for BN ; BW ; BP are presented in Sections 6.1 and 6.2, whereas Sec-
tion 6.3 provides estimates for the structural parameters �A; ��:The next two Sections present
the data sources and empirical strategy employed in the estimation.
4 Data Sources
I assemble an unbalanced panel of urban footprints-years, covering all Indian cities for which a
footprint could be retrieved based on the methodology explained below.
4.1 Urban Footprints
I retrieve the boundaries of urban footprints from two sources. The �rst is the U.S. Army India
and Pakistan Topographic Maps (U.S. Army Map Service, 195?), a series of detailed maps
covering the entire Indian subcontinent at a 1:250,000 scale. I geo-referenced these maps and
traced the reported perimeter of urban areas, which are clearly demarcated (Figure 1).
The second source is derived from the DMSP/OLS Night-time Lights dataset. This dataset
14
is based on night-time imagery recorded by satellites from the U.S. Air Force Defense Meteo-
rological Satellite Program (DMSP) and reports the recorded intensity of Earth-based lights,
measured by a six-bit number (ranging from 0 to 63). These data are reported for every year
between 1992 and 2010, with a resolution of 30 arc-seconds (approximately 1 square kilome-
ters). Night-time lights have been employed in economics typically for purposes other than
urban mapping (Henderson et al., 2012). However, the use of the DMSP/OLS dataset for de-
lineating urban areas is quite common in urban remote sensing (Henderson et al., 2003; Small,
2005; Small et al. 2011). The basic methodology is the following: �rst, I overlap the night-time
lights imagery with a point shape�le with the coordinates of Indian settlement points, taken
from the Global Rural-Urban Mapping Project (GRUMP) Settlement Points dataset (CIESIN
et al., 2011; Balk et al., 2006). I then set a luminosity threshold (e.g. 35) and consider spatially
contiguous lighted areas surrounding the city coordinates with luminosity above that thresh-
old. This approach, illustrated in Figure 2, can be replicated for every year covered by the
DMSP/OLS dataset.
The choice of luminosity threshold results in a more or less restrictive de�nition of urban
areas, which will appear larger for lower thresholds4. To choose luminosity thresholds appropri-
ate for India, I overlap the 2010 night-time lights imagery with available Google Earth imagery.
I �nd that a luminosity threshold of 35 generates the most plausible mapping for those cities
covered by both sources5. In my full panel (including years 1950 and 1992-2010), the average
city footprint occupies and area of approximately 63 squared kilometers6.
Using night-time lights as opposed to alternative satellite-based products, in particular day-
time imagery, is motivated by a number of advantages. Unlike products such as aerial pho-
tographs or high-resolution imagery, night-time lights cover systematically the entire Indian
4Determining where to place the boundary between urban and rural areas always entails some degree of
arbitrariness, and in the urban remote sensing literature there is no clear consensus on how to set such threshold.
It is nevertheless recommended to validate the chosen threshold by comparing the DMSP/OLS-based urban
mapping with alternative sources, such as high-resolution day-time imagery, which in the case of India is
available only for a small subset of city-years.5For years covered by both sources (1990, 1995, 2000), my maps also appear consistent with those from the
GRUMP - Urban Extents Grid dataset, which combines night-time lights with administrative and Census data
to produce global urban maps (CIESIN et al., 2011; Balk et al., 2006).6My results are robust to using alternative luminosity thresholds between 20 and 40. Results are available
upon request.
15
subcontinent, and not only a selected number of cities. Moreover, they are one of the few
sources which allow to detect changes in urban areas over time, due to their yearly temporal
frequency. Finally, unlike multi-spectral satellite imagery such as Landsat- or MODIS- based
products, which in principle would be available for di¤erent points in time, night-time lights
do not require any sophisticated manual pre-processing7. An extensive portion of the urban
remote sensing literature compares the accuracy of this approach in mapping urban areas with
that attainable with alternative satellite-based products, in particular day-time imagery (in-
ter alia, Henderson et al, 2003; Small et al., 2005). This cross-validation exercise has been
carried out also speci�cally in the context of India by Joshi et al. (2011) and Roychowdhury
(2009). The general takeout is that none of these sources is error-free, and that there is no
strong case for preferring day-time over night-time satellite imagery if aerial photographs are
not systematically available for the area to be mapped.
It is well known that urban maps based on night-time lights will tend to in�ate urban
boundaries, due to "blooming" e¤ects (Small et al., 2005)8. This can only partially be limited
by setting high luminosity thresholds. In my panel, urban footprints as reported for years
1992-2010 thus re�ect a broad de�nition of urban agglomeration, which typically goes beyond
the current administrative boundaries. This contrasts with urban boundaries reported in the
US Army maps, which seem to re�ect a more restrictive de�nition of urban areas (although
no speci�c documentation is available). Throughout my analysis I include year �xed e¤ects,
which amongst other things control for these di¤erences in data sources, as well as for di¤erent
calibrations of the night-time lights satellites.
By combining the US Army maps (1950s) with yearly maps obtained from the night-time
lights dataset (1992-2010) I thus assemble an unbalanced panel of urban footprints9. The criteria
7Using multi-spectral imagery to map urban areas requires a manual classi�cation process, which relies
extensively on alternative sources, mostly aerial photographs, to cross-validate the spectral recognition, and is
subject to human bias.8DMSP-OLS night-time imagery has a tendency to overestimate the actual extent of lit area on the ground,
due to a combination of coarse spatial resolution, overlap between pixels, and minor geolocation errors (Small
et al., 2005).9The resulting panel dataset is unbalanced for two reasons: �rst, some settlements become large enough to
be detectable only later in the panel; second, some settlements appear as individual cities for some years in
the panel and then become part of larger urban agglomerations in later years.The number of cities in the panel
ranges from 352 to 457, depending on the year considered.
16
for being included in the analysis is to appear as a contiguous lighted shape in the night-time
lights dataset. This appears to leave out only very small settlements. Throughout my analysis,
I instrument all the geometric properties of urban footprints, including both area and shape.
This IV approach addresses problems of non-classical measurement error which could a¤ect my
data sources, for instance due to the well-known correlation between income and luminosity.
4.2 Shape Metrics
The indicators of city shape which I employ, based on those in Angel, Civco and Parent (2010)10,
are used in landscape ecology and urban studies to proxy for within-city trips and infer travel
costs. They are all based on the distribution of points around the polygon�s centroid11 or within
the polygon, and are measured in kilometers. Summary statistics for the indicators below are
reported in Table 1.
(i) The remoteness index is the average distance between all interior points and the centroid.
It can be considered a proxy for the average length of commutes to the urban center.
(ii) The spin index is computed as the average of the squared distances between interior
points and centroid. This is similar to the remoteness index, but gives more weight to the
polygon�s extremities, corresponding to the periphery of the footprint. This index is more
capable of identifying footprints that have "tendril-like" projections, often perceived as an
indicator of sprawl.
(iii) The disconnection index captures the average distance between all pairs of interior
points. It can be considered a proxy for commutes within the city, without restricting one�s
attention to those leading to the center.
(iv) The range index captures the maximum distance between two points on the shape
perimeter, representing the longest possible of commute trips within the city.
All these measures are mechanically correlated with polygon area. In order to separate the
e¤ect of geometry per se from that of city size, in my preferred speci�cations I explicitly control
for the area of the footprint - which is separately instrumented for. Conditional footprint area,
10I am thankful to Vit Paszto for help with the ArcGis shape metrics routines. I have renamed some of the
shape metrics for ease of exposition.11The centroid of a polygon, or center of gravity, is the point which minimizes the sum of squared Euclidean
distances between itself and each vertex.
17
higher values of these indexes indicate longer within-city trips. Alternatively,it is possible to
normalize each of these indexes, computing a version which is invariant to the area of the
polygon. I do so by computing �rst the radius of the "Equivalent Area Circle" (EAC), namely
a circle with an area equal to that of the polygon. I then normalize the index of interest dividing
it by the EAC radius, obtaining what I de�ne normalized remoteness, normalized spin, etc. One
way to interpret these normalized metrics is as deviations of a polygon�s shape from that of a
circle, the shape which minimizes all the indexes above.
Figure 3 provides a visual example of how these metrics map to the shape of urban foot-
prints. Among million-plus cities, I consider those with respectively the "best" and the "worst"
geometry based on the indicators described above, namely Bengaluru and Kolkata (formerly
known as Bangalore and Calcutta). The �gure reports the footprints of the two cities as of year
2005, where Bengaluru�s footprint has been rescaled so that they have the same area. The
�gure also reports the above shape metrics computed for these two footprints. The di¤erence
in the remoteness index between Kolkata and (rescaled) Bengaluru is 4.5 km; the di¤erence
in the disconnection index is 6.2 km. The interpretation is the following: if Kolkata had the
same compact shape that Bengaluru has, the average trip to the center would be shorter by
4.5 km and the average trip within the city would be shorter by 6.2 km. The Indian Ministry
of Urban Development (2008) estimates the average commute speed in million-plus cities to be
of 12 km per hour in 2011, which is predicted to become 9 km by 2021. According to the 2011
estimated speed, the above di¤erences in trip length translate to a di¤erence in commute times
of respectively 22.5 minutes (average trip to the center) and 31 minutes (average within-city
trip). Although this is a very rough calculation, it is nevertheless revealing that city geometry
indeed has potentially sizeable impacts on commute times.
4.3 Geography
Following Saiz (2011), I consider as "undevelopable" terrain which either covered by a water
body or is characterized by a slope above 15%. I draw upon the highest resolution sources
available: the Advanced Spaceborne Thermal Emission and Re�ection Radiometer (ASTER)
Global Digital Elevation Model (NASA and METI, 2011), with a resolution of 30 meters, and
the Global MODIS Raster Water Mask (Carroll et al. 2009), with a resolution of 250 meters. I
combine these two raster datasets to classify pixels as "developable" or "undevelopable". Figure
18
4 illustrates this classi�cation for the Mumbai area.
4.4 Population and Other Census Data
City-level data for India is notoriously hard to obtain (Greenstone and Hanna, forthcoming).
The only systematic source which collects data explicitly at the city level is the Census of
India, conducted every 10 years. In this project I employ population data from Census years
1871-2011. As explained in Section 5.1, historic population (1871-1941) is used to construct
one of the two versions of my instrument, whereas population drawn from more recent waves
(1951, 1991, 2001 and 2011) is used as an outcome variable12.
Outcomes other than population are not consistently available for all Census years. I draw
data on urban road length in 1991 from the 1991 Town Directory. In recent Census waves
(1991, 2001, 2011) data on slum population and physical characteristics of houses are available
for a subset of cities.
It is worth pointing out that "footprints" as retrieved from the night-time lights dataset do
not always have an immediate Census counterpart in terms of town or urban agglomeration, as
they sometimes stretch to include suburbs and towns treated as separate units by the Census.
A paradigmatic example is the Delhi conurbation, which as seen from the satellite expands
well beyond the administrative boundaries of the New Delhi National Capital Region. When
assigning population totals to an urban footprint, I sum the population of all Census settlements
which are located within the footprint, thus computing a "footprint" population total13.
4.5 Wages and Rents
For outcomes other than those available in the Census I rely on the National Sample Survey
and the Annual Survey of Industries, which provide at most district identi�ers. I thus follow the
approach of Greenstone and Hanna (forthcoming): I match cities to districts and use district
urban averages as proxies for city-level averages. It should be noted that the matching is not
12Historic population totals were taken from Mitra (1980). Census data for years 1991 to 2001
were taken from the Census of India electronic format releases. 2011 Census data were retrieved from
http://www.censusindia.gov.in/DigitalLibrary/Archive_home.aspx.13In order to assemble a consistent panel of city population totals over the years I also take into account
changes in the de�nitions of "urban agglomerations" and "outgrowths" across Census waves.
19
always perfect, for a number of reasons. First, it is not always possible to match districts as
reported in these sources to Census districts, and through these to cities, due to redistricting
and inconsistent numbering throughout this period. Second, there are a few cases of large
cities which cut across districts (e.g. Hyderabad). Finally, there are a number of districts
which contain more than one city from my sample. In these cases I follow several matching
approaches: considering only the main city for that district, and dropping the district entirely.
I show results following both approaches. The matching process introduces considerable noise
and leads to results which are relatively less precise and less robust than those I obtain with
city-level outcomes.
Data on wages are taken from the Annual Survey of Industries (ASI), waves 1990, 1994, 1995,
1997, 1998, 2009, 201014. These are repeated cross-sections of plant-level data collected by the
Ministry of Programme Planning and Implementation of the Government of India. The ASI
covers all registered manufacturing plants in India with more than �fty workers (one hundred
if without power) and a random one-third sample of registered plants with more than ten
workers (twenty if without power) but less than �fty (or one hundred) workers. As mentioned
by Fernandes and Sharma (2012) amongst others, the ASI data are extremely noisy in some
years, which introduces a further source of measurement error. The average individual yearly
wage in this panel amounts to 94 thousand Rs. at current prices.
Unfortunately there is no systematic source of data for property prices in India. I construct
a rough proxy for the rental price of housing drawing upon the National Sample Survey (House-
hold Consumer Expenditure schedule), which asks households about the amount spent on rent.
In the case of owned houses, an imputed �gure is provided. I focus on rounds 62 (2005-2006),
63 (2006-2007) and 64 (2007-2008), since they are the only ones for which the urban data is
representative at the district level and which report total dwelling �oor area as well. I use this
information to construct a measure of rent per square meter. The average yearly total rent paid
in this sample amounts to about 25 thousand Rs., whereas the average yearly rent per squared
meter is 603 Rs., at current prices. These �gures are likely to be underestimating the market
rental rate, due to the presence of rent control provisions in most major cities of India (Dek,
2006). To cope with this problem, I also construct an alternative proxy for housing rents which
focuses on the upper half of the distribution of rents per meter, which is less likely to include
14These are all the waves I could access as of June 2014.
20
observations from rent-controlled housing.
4.6 Other Data
Data on state-level infrastructure (motor vehicles density, state urban roads length) is taken
from the Ministry of Road Transport and Highways, Govt. of India.
Data on the current road network is constructed from the maps available on Openstreetmap15,
a collaborative mapping project which provides crowdsourced maps of the world. Open-
streetmap data has been favorably compared with proprietary data sources and is continuously
updated. As such, it re�ects the current state of the street network. I consider the most recent
night-time lights-based map of urban boundaries in my sample - corresponding to 2010 - and
overlap it with the street network map of India provided by Openstreetmap. Information on
the type of road - whether trunk, residential, secondary etc. - is also provided. Given the
collaborative nature of Openstreetmap, there is a concern that the level of detail of such maps
might be higher in larger cities, or in neighborhoods with more economic activity. Upon visual
inspection, it appears that smaller roads are reported only in relatively bigger cities. To avoid
this source of non-classical measurement error, I exclude small roads and focus on those denoted
as "trunk", "primary" or "secondary". I then compute the total road length by considering
street segments contained within the urban boundary. The average road density in my sample
as of year 2010, obtained by dividing total city road length by footprint area, is 2.4 km per
squared km. Given the tendency of night-time lights to overestimate urban boundaries, this
�gure should be considered an underestimate of the actual road density.
Data on the maximum permitted Floor Area Ratios for a small cross-section of Indian cities
(55 cities in my sample) is taken from Sridhar (2010), who collected them from individual
urban local bodies as of the mid-2000s. FARs are expressed as ratios of the total �oor area of
a building over the area of the plot on which it sits. The average FAR in this sample is 2.3, a
very restrictive �gure compared to international standards. For a detailed discussion of FARs
in India, see Sridhar (2010) and Bertaud and Brueckner (2005).
Data on the location of productive establishments in year 2005 is derived from the urban
Directories of Establishments pertaining to the 5th Economic Census. The Economic Census
15http://www.openstreetmap.org/about
21
is a complete enumeration of all establishments, with the exception of those involved in crop
production, conducted by the Indian Ministry of Statistics and Programme Implementation.
Town or district identi�ers are not provided to the general public. However in year 2005 estab-
lishments with more than 10 employees were required to provide an additional "address slip",
containing a complete address of the establishment, year of initial operation and employment
class. I geo-referenced all the addresses corresponding to cities in my sample through Google
Maps API, retrieving consistent coordinates for about 240 thousand establishments in about
200 footprints. Although limited by their cross-sectional nature, these data provide an oppor-
tunity to study the spatial distribution of employment within cities. As a �rst, exploratory
step in this direction I compute a simple measure of spatial concentration based on Moran�s
I statistic (Anselin, 1995), which has been used as an indicator of city "compactness" (Tsai,
2005).
5 Empirical Strategy
The objective of my empirical analysis is to estimate the e¤ects of city shape on a number of
city-year level outcomes, most notably population, wages and rents. My data has the structure
of an unbalanced city-year panel. In every year, I observe the geometric properties of the
footprint of each city, namely footprint area and the di¤erent shape metrics described above.
The goal is to estimate the relationship between shape in a given city-year on a number of city-
year level outcomes, conditional on city and year �xed e¤ects. This strategy exploits variation
in urban shape which is both cross-sectional and temporal. City and year �xed e¤ects are
included in all speci�cations, so as to account for time-invariant city characteristics and for
country-level trends in population and other outcomes. The identi�cation of the impacts of
shape thus relies on comparing changes in urban shape over time for each city16.
16As discussed below, a limited number of outcomes, analyzed in Section 7, are available only for a cross-
section of cities. In these cases, I resort to a cross-sectional version of equation (39), which cannot include city
�xed e¤ects.
22
5.1 Instrument Construction
A major concern in estimating the above relationship is the endogeneity of city geometry.
The observed urban footprint at a given point in time is the result of the interaction of local
geographic conditions, city growth and policy. Cities which experience faster population growth
might be expanding in a more chaotic and unplanned fashion, generating a "leapfrog" pattern of
development which translates into less compact shapes. At the same time, cities which exhibit
faster growth rates might be the object of more stringent regulations. For instance, restrictive
Floor Area Ratios in India have been motivated by a perceived need to reduce urban densities
(Sridhar, 2010). In order to address this endogeneity problem, I employ an IV approach,
constructing an instrument for city shape which varies at the city-year level.
My instrument is constructed combining geography with a mechanical model for city expan-
sion in time. The underlying idea is that as cities expand in space over time, they hit di¤erent
geographic obstacles which constrain their shapes by preventing expansion in some of the possi-
ble directions. I instrument the actual shape of the observed footprint at a given point in time
with the potential shape which the city can have, given the geographic constraints which it faces
at that stage of its predicted growth. More speci�cally, I consider the largest contiguous patch
of land which is developable, i.e. not occupied by a water body nor by steep terrain, within a
given predicted radius around each city. I denote this contiguous patch of developable land as
"potential footprint". I compute the shape properties of the potential footprint and use them
as instruments for the corresponding shape properties of the actual urban footprint. What
gives time variation to this instrument is the fact that the predicted radius is time-varying, and
expands over time based on a mechanical model for city expansion. In its simplest form this me-
chanical model postulates a common growth rate for all cities; in my benchmark speci�cations,
it is city-speci�c, and based on each city�s projected historic population.
The procedure for constructing the instrument is illustrated in Figure 5 for the city of
Mumbai. Recall that I observe the footprint of a city c in year 195117 (from the U.S. Army
Maps) and then in every year t between 1992 and 2010 (from the night-time lights dataset).
I take as starting point the minimum bounding circle of the 1951 city footprint (Figure 5a).
17The US Army Maps are from the mid-50s, but no speci�c year of publication is provided. The closest
Census year is 1951. For the purposes of constructing the city-year panel, I am attributing to the footprints
observed in these maps the year 1951, so that I can match them to population as of Census year 1951.
23
To construct the instrument for city shape in 1951, I consider the portion of land which lies
within this bounding circle and is developable, i.e. not occupied by water bodies nor steep
terrain. The largest contiguous patch of developable land within this radius is colored in green
in Figure 5b and represents what I de�ne as "potential footprint" of the city of Mumbai in 1951.
In subsequent years t 2 f1992; 1993:::; 2010g I consider concentrically larger radii brct around thehistoric footprint, and construct corresponding potential footprints lying within these predicted
radii (Figures 5c and 5d).
To complete the description of the instrument I need to specify how brct is determined. Theprojected radius brct is obtained by postulating a simple, mechanical model for city expansionin space. I consider two versions of this model: a "city-speci�c" version and a "common rate"
one.
(A) City-speci�c: In this �rst version of the model, I make the rate of expansion of brct varyacross cities, depending on their historic (1871 - 1951) population growth rates. In particular,brct answers the following question: if the city�s population continued to grow as it did between1871 and 1951 and population density remained constant at its 1951 level, what would be the
area occupied by the city in year t? More formally, the steps involved are the following:
(i) I project log-linearly the 1871-1951 population of city c (from the Census) in all subse-
quent years, obtaining the projected population [popc;t , for t 2 f1992; 1993:::; 2010g :(ii) Denote the area of city c�s actual footprint in year t as areac;t and the actual - not
projected - population of city c in year t as popc;t. I pool together the 1951-2010 panel of cities
and run the following regression:
log(areac;t) = � � log([popc;t) + � � log�popc;1950areac;1950
�+ t + "c;t (39)
from which I obtain \areac;t, the predicted area of city c in year t.
(iii) I compute crc;t as the radius of a circle with area \areac;t:crc;t =r\areac;t
�: (40)
The interpretation of the circle with radius crc;t from �gures 5c and 5d is thus the following: thisis the area which the city would occupy if it continued to grow as in 1871-1951, if its density
remained the same as in 1951, and if the city could expand freely and symmetrically in all
directions, in a fashion which optimizes the length of within-city trips.
24
(B) Common-rate: The second version of the mechanical model is even more parsimo-
nious: the rate of expansion of the radii is the same for all cities, and equivalent to the average
expansion rate across all cities in the sample. More formally, I run the following regression:
log(areac;t) = �c + t + "c;t (41)
where �c and t denote city and year �xed e¤ects, from which I retrieve an alternative version
of \areac;t and corresponding crc;t = q \areac;t�:
This instrument seeks to isolate the variation in urban geometry which is induced by geog-
raphy, excluding the variation which results from policy or other endogenous choices. Although
resorting to geography arguably helps addressing issues of policy endogeneity, there is neverthe-
less a concern that geography a¤ects location choices directly, for instance through the inherent
amenity (or disamenity) value of water bodies, and not only through the constraints it posits
on urban form. These concerns are mitigated by two features of my instrument. First, it is
not purely cross-sectional but has time variation. This allows me to control for time-invariant
e¤ects of geography through city �xed e¤ects. Second, it captures a very speci�c feature of ge-
ography: whether it allows for compact development or not. My instrument is not based on the
generic presence of topographic constraints, nor on the share of constrained over developable
terrain. Rather, it measures the geometry of available land. In one of my robustness checks, I
show that my results are unchanged when I exclude mountain and coastal cities, which would
be the two most obvious examples of cities where geography might have a speci�c (dis)amenity
value.
5.2 Estimating Equations
Consider a generic shape metric S - which could be any of the indexes discussed in Section 4.2.
Denote with Sc;t the shape metric computed for the actual footprint observed for city c in year
t, and with fSc;t the shape metric computed for the potential footprint of city c in year t, namelythe largest contiguous patch of developable land within the predicted radius crc;t:Speci�cation I
Consider outcome variable Y 2 (N;W; pH) and let areac;t be the area of the urban footprint.My benchmark estimating equation (Speci�cation I) corresponds to equation (31) in the model
25
outlined in Section 3, augmented with city and year �xed e¤ects:
log(Yc;t) = a � Sc;t + b � log(areac;t) + �c + �t + �c;t (42)
This equation contains two endogenous regressors: Sc;t and log(areac;t). These are instrumented
using respectively fSc;t and log([popc;t) - the same projected historic population used in the city-speci�c model for urban expansion, step i.
This results in the following two �rst-stage equations:
Sc;t = � � fSc;t + � � log([popc;t) + !c + 't + �c;t (43)
and
log(areac;t) = � � fSc;t + � � log([popc;t) + �c + t + "c;t: (44)
The counterpart of log(areac;t) in the conceptual framework is log(L), where L is the amount
of land which regulators allow to be developed in each period. It is plausible that regulators set
this amount based on projections of past city growth, which rationalizes the use of projected
historic population as an instrument.
One advantage of this approach is that it allows me to analyze the e¤ects of shape and
area considered separately - recall that the non-normalized shape metrics are mechanically
correlated with footprint size. However, a drawback of this strategy is that it requires not only
an instrument for shape, but also one for area.
Speci�cation II
For robustness, I consider also an alternative approach which does not explicitly include city
area in the regression, and therefore does not require including projected historic population
among the instruments.
When focusing on population as an outcome variable, a natural way to do this is to normalize
both right- and left-hand side by city area, considering respectively the normalized shape metric
- see Section 4.2 - and population density. This results in the following, more parsimonious
speci�cation (Speci�cation II): de�ne population density18 as
dc;t =popc;tareac;t
18Note that this does not coincide with population density as de�ned by the Census, which re�ects adiminis-
trative boundaries.
26
and denote the normalized version of shape metric S with nS. The estimating equation becomes
dc;t = a � nSc;t + �c + �t + �c;t (45)
which contains endogenous regressor nSc;t. I instrument nSc;t with]nSc;t, namely the normalized
shape metric computed for the potential footprint. The corresponding �rst-stage equation is
nSc;t = � �]nSc;t + �c + t + "c;t: (46)
The same approach can be followed for other outcome variables representing quantities -
such as road length. Although it does not allow the e¤ects of shape and area to be separately
identi�ed, this approach is less demanding. In particular, it does not require using projected
historic population, and allows me to construct my shape instrument using both versions ofcrc;t, the one obtained from the city-speci�c model as well as that obtained from the common
rate model (see Section 5.1).
While population or road density are meaningful outcomes per se, it does not seem as natural
to normalize factor prices - wages and rents - by city area. For these other outcome variables,
the more parsimonious alternative to Speci�cation I takes the following form:
log(Yc;t) = a � Sc;t + �c + �t + �c;t (47)
where Y 2 (W; pH):This equation does not explicitly control for city area other than throughcity and year �xed e¤ects. Again, the endogenous regressor Sc;t is instrumented using fSc;t,resulting in the following �rst-stage equation:
Sc;t = � � fSc;t + !c + 't + �c;t: (48)
All of the speci�cations discussed above include year and city �xed e¤ects, which capture
time-invariant city characteristics - including the general e¤ect of geography. The identi�cation
of the impacts of shape thus relies on comparing geography-driven changes in urban shape over
time for each city19. Although the bulk of my analysis, presented in Section 6, relies on both
19The implicit underliying assumption of this approach is a "parallel trends" one, which would be violated
if outcomes in cities with di¤erent geometries followed di¤erential trends. To mitigate this concern, in one of
my robustness checks (Appendix Tables 1 and 2) I augment the speci�cations above with year �xed e¤ects
interacted with the city�s shape at the beginning of the panel.
27
cross-sectional and temporal variation, a limited number of outcomes, analyzed in Section 7,
are available only for a cross-section of cities. In these cases, I resort to cross-sectional versions
of equations (43) to (49),which cannot include city �xed e¤ects.
In all speci�cations I employ robust standard errors clustered at the city level, to account
for arbitrary serial correlation over time in cities.
6 Empirical Results: Amenity Value of City Shape
In this Section I address empirically the question of how city shape a¤ects the spatial equilibrium
across cities. The predictions of the conceptual framework suggest that, if city shape is valued as
a consumption amenity by consumers, cities with longer trip patterns should be characterized
by lower population, higher wages and lower rents.
6.1 First Stage
[Insert Table 2]
Table 2 presents results from estimating the �rst-stage relationship between city shape and
the geography-based instrument described in Section 5.1. Each observation is a city-year.
Panels, A, B, C and D each correspond to one of the four shape metrics discussed in Section
4.2: respectively, remoteness, spin, disconnection and range20.Higher values of these indexes
represent less compact shapes. Summary statistics are reported in Table 1. Columns 1 and 2
report the �rst stage for footprint shape (eq. (44)) and area (eq. (45)), which are relevant for
Speci�cation I. The dependent variables are city shape, measured in km and log city area, in
km2. The corresponding instruments are the shape of the potential footprint and log projected
historic population, as described in Section 5.2. The construction of the potential footprint
is based on the city-speci�c model for city expansion discussed in Section 5.1. Column 3
reports the �rst-stage for normalized shape (eq. (47)), which is the explanatory variable used
in Speci�cation II. Recall that normalized shape is an area-invariant measure of shape obtained
normalizing a given shape metric by footprint radius. In this speci�cation the construction of
20Recall that remoteness (panel A) is the average squared length of trips to the centroid; spin (panel B) is
the average squared length of trips to the centroid; disconnection (panel C) is the average length of within-city
trips; range (panel D) is the maximum length of within-city trips.
28
the potential footprint is based on the "common rate" model for city expansion outlined in
Section 5.1.
Let us consider �rst Table 2A, which reports speci�cation I estimated for the remoteness
index. As discussed in Section 4.2, this index captures the length of the average trip to the
footprint�s centroid, and can be considered a proxy for the average commute to the central
business district. Both �rst stages appear strong: the remoteness of the potential footprint is a
highly signi�cant predictor of the remoteness index computed for the actual footprint. Similarly,
in column 2, projected historic population predicts footprint area. Column 2 reveals another
interesting pattern: the area of the actual footprint is positively a¤ected by the remoteness
of the potential footprint. While this partly re�ects the mechanical correlation between shape
metric and footprint area, it also suggests that cities which are surrounded by topographic
obstacles tend to expand more in space. An interpretation of this result is that the presence of
topographic constraints induces a leapfrog development pattern, which is typically more land-
consuming. It could also re�ect an inherent di¢ culty in planning land-e¢ cient development
in constrained contexts, which could result in less parsimonious land use patterns. The �rst-
stage of the more parsimonious Speci�cation II, presented in column 3, is also strong: the
normalized shape of the potential footprint is a signi�cant predictor of the normalized shape of
the actual footprint. The approach followed in column 3 is not based on projections of historic
city population, and relies on the "common-rate" model for city expansion outlined in Section
5.1.21 The results for the remaining shape indicators, reported in panels B, C, and D, are
qualitatively similar.
6.2 Population
[Insert Table 3]
My main results on population and city shape are reported in Table 3. As in Table 2, each
observation is a city-year and each panel corresponds to a di¤erent shape metric. Column 1
reports the IV results from estimating Speci�cation I (equation (43)), which links population
to city area and shape, separately instrumented for. The corresponding �rst stage is reported
21The normalized shape instrument can in principle be constructed also using the city-speci�c model for urban
expansion. Results of the corresponding �rst-stage are not reported in the table for brevity, but are qualitatively
similar to those in column 3 and are available upon request.
29
in column 1 of Table 2. Column 3 reports the corresponding OLS estimates. Column 2 reports
the IV results from estimating Speci�cation II (equation (46). The corresponding �rst stage is
reported in column 3 of Table 2.
Interestingly, the OLS relationship between population and shape, conditional on area (col-
umn 3) appears to be positive due to an equilibrium correlation between city size and bad
geometry: larger cities are typically also less compact. This arises from the fact that an ex-
panding city has a tendency to deteriorate in shape. The intuition for this is the following: a
new city typically arises in a relatively favorable geographic location; as it expands in space,
however, it inevitably reaches areas with less favorable geography. Once shape is instrumented
by geography (column 1), less compact cities are associated to a decrease in population, condi-
tional on (instrumented) area, city and year �xed e¤ects. To understand the magnitudes of this
e¤ect,consider the remoteness index (panel A), representing the length in km of the average trip
to the footprint�s centroid. A one-standard deviation in normalized remoteness (0.06) for the
average-sized city (which has radius 4.5 km) corresponds to roughly 0.26 kilometers. Holding
constant city area, a 0.26 kilometer increase in the average trip to the centroid is approximately
associated to a 3% decline in population.
Column 2 reports results obtained from the more parsimonious Speci�cation II, which links
population density, measured in thousand inhabitants per km2, to (instrumented) normalized
shape. Recall that normalized shape metrics capture the departure of a city�s shape from an
ideal circular shape and are invariant to city area, higher values implying longer trips. The
IV estimates of Speci�cation II indicate that less compact cities are associated to a decline in
population density. The magnitudes of this e¤ect are best understood in terms of standardized
coe¢ cients. According to the estimates in panel A, a one standard deviation increase in nor-
malized remoteness is associated to a decline in population density of 0.9 standard deviations.
The results obtained with Speci�cation I (Table 3, column 1) together with the �rst-stage es-
timates in Table 2 (column 2) indicate that this decline in density is driven both by a decrease
in population and by an increase in footprint area.
The results for the remaining shape indicators, reported in panels B, C, and D, are qual-
itatively similar. The fact that these indexes are mechanically correlated with one another
prevents me from including them all in the same speci�cation. However, a comparison of the
magnitudes of the IV coe¢ cients of di¤erent shape metrics on population suggests that the
most salient spatial properties are remoteness (Table 3A) and disconnection (Table 3C), which
30
capture respectively the average trip length to the centroid and the average trip length within
the footprint. This is plausible, since these two indexes are those which more closely proxy for
urban commute patterns. Non-compactenss in the periphery, captured by the spin index (Table
3B), appears to have a precise zero e¤ect on population. The e¤ect of the range index (Table
3D), capturing the longest possible trip within the footprint, is signi�cant but small in mag-
nitude. For brevity, in the rest of my analysis I will mostly focus on the disconnection index,
which measures the average within-city trip without restring one�s attention to trips leading
to the centroid. This index is the most general indicator for within-city commutes, and seems
suitable to capture trip patters in polycentric as well as monocentric cities. Unless otherwise
speci�ed, in the rest of the tables "shape" will indicate the disconnection index.
[Insert Table 4]
As a robustness check, in Table 4 I re-estimate Speci�cation I, excluding from the sample
cities with severely constrained topographies, namely those located on the coast or in high-
altitude areas. Such cities make about 9 % of cities in my sample. Out of 457 cities in
the initial year of the panel (1951), those located on the coast and in mountainous areas are
respectively 24 and 17 Both the �rst-stage (columns 1, 2, 4 and 5) and the IV estimates of
the e¤ect of shape on population (columns 3 and 6) are minimally a¤ected by excluding these
cities. This shows that my instrument has explanatory power also in cities without extreme
topographic constraints22, and that my IV results are not driven by a very speci�c subset of
compliers.
Another robustness check is provided in Appendix Table 1. I re-estimate the IV impact
of shape on population and density (columns 1 and 2 from Table 3C), including year �xed
e¤ects interacted with each city�s shape at the beginning of the panel. This more conservative
speci�cation allows cities with di¤erent initial geometries to follow di¤erent time trends. Results
are qualitatively similar to those obtained in Table 3. This mitigates the concern that diverging
trends across cities with di¤erent geometries might be confounding the results.
22Recall that my instrument - the shape of the "potential" footprint - is not based on the severity of topo-
graphic constraints nor on the total share of land lost to such constraints, but is mostly driven by the relative
position of constrained pixels.
31
6.3 Wages and Rents
The results presented thus far seem to indicate that consumers are a¤ected by city shape in their
location choices and that they dislike non-compact shapes. A natural question which arises next
is whether we can put a price on "good shape". As discussed in Section 3, the Rosen-Roback
model provides a framework for doing so by showing how urban amenities are capitalized in
wages and rents. In particular, the model predicts that cities with better consumption amenities
should be characterized by higher rents and lower wages.
Results on wages and rents are reported in Tables 5 and 6 respectively. As I discuss in Section
4.5, the measures of wages and rents which I employ are subject to signi�cant measurement
error. Both are urban district-level averages, derived respectively from the Annual Survey of
Industries and the National Sample Survey Consumer Expenditure Schedule. The matching
between cities and districts in not one-to-one. In particular, there are numerous instances of
districts which include more than one city. I cope with these cases following three di¤erent
approaches: (i) ignore the issue and keep in the sample all cities; (ii) drop from the sample
districts with more than one city, thus restricting my sample to cities which have a one-to-one
correspondence with districts; (iii) include in the sample only the largest city in each district.
Tables 5 and 6 report estimation results obtained from all three approaches.
[Insert Table 5]
In Table 5 I report the OLS and IV relationship between average wages and city shape. The
dependent variable is the log urban average of individual yearly wages in the city�s district, in
thousand 2014 Rupees. Columns 1, 4 and 7 report the IV results from estimating Speci�cation
I (equation (43)), which is conditional on instrumented city area. Columns 3, 6 and 9 report the
same speci�cation, estimated by OLS. Columns 2, 5 and 8 report the IV results from estimating
Speci�cation II (equation 48), which does not explicitly control for city area. The construction
of the potential footprint is based on the city-speci�c model for city expansion in columns 1, 4
and 7, and on the common rate one in column 2, 5, 8 �see Section 5.1.
These estimates indicate that less compact shapes, as captured by higher values of the dis-
connection index, are associated to higher wages both in the OLS and in the IV. This pattern is
consistent across di¤erent speci�cations and city-district matching approaches. Appendix Table
2, panel A, shows that these results are also robust to including year �xed e¤ects interacted by
32
initial shape. This positive estimated impact is compatible with the interpretation that con-
sumers are paying a premium in terms of foregone wages in order to live in cities with better
shapes. Moreover, it suggests that city shape is more a consumption than it is a production
amenity. When city area is explicitly included in the regression, the reduced-form relationship
between area and wages is negative, as predicted by the conceptual framework (condition 17 in
Section 3).
[Insert Table 6]
Tables 6 reports the same set of speci�cations for house rents. In panel A the dependent
variable considered is the log of yearly housing rent per square meter, in 2014 Rupees, averaged
throughout all urban households in the district. In panel B the dependent variable is analogous,
but constructed averaging only the upper half of the distribution of urban housing rents in each
district. This addresses the concern that reported rents are a downward-biased estimate of
market rents due to rent control policies. These estimates appear noisy or only borderline
signi�cant, with p values between 0.10 and 0.15. However, a consistent pattern emerges: the
impact of disconnected shape on rents is negative in the IV and close to zero, or possibly
positive, in the OLS. Appendix Table 2, panel B, shows that these results are qualitatively
similar including year �xed e¤ects interacted by initial shape. This is consistent with the
interpretation that consumers are paying a premium in terms of higher housing rents in order
to live in cities with better shapes. The reduced-form relationship between city area and rents
is also negative, consistent with the conceptual framework (condition 18 in Section 3).
6.4 Interpreting estimates through the lens of the model
Tables 3, 5 and 6 provide estimates for the reduced-form relationship between city shape and
respectively log population, wages and rents, conditional on city area. Although results for
wages and rents should be interpreted with caution due to the data limitations discussed above,
the signs of the estimated coe¢ cients are consistent with the interpretation that consumers view
compact shape as an amenity. In this sub-section I use these reduced-form estimates to back
out the implied welfare loss associated to poor city geometry, according to the model outlined
in Section 3. I focus here on the disconnection index, representing the average commute within
the footprint. All monetary values are expressed in 2014 Rupees.
33
Recall that a one-unit increase in shape metric S has a welfare e¤ect equivalent to a decrease
in income of �� log points, which, as derived in Section 3 (eq. 38) can be estimated as
b�� = �cBP �dBWwhere � is the share of consumption spent on housing.
My most conservative point estimates for dBW and cBP , from Speci�cation II as estimated
in Tables 5 and 6A respectively, amount to 0:038 and �0:518. To calibrate �, I compute theshare of household expenditure devoted to housing for urban households, according to the NSS
Household Consumer Expenditure Survey data in my sample - this �gure amounts to 0:16. The
implied b�� is �0:14. This implies that a one standard deviation increase in disconnection forthe average-sized city (about 360 meters) entails a welfare loss equivalent to a 0:05 log points
decrease in income.
It is interesting to compare this �gure with the actual cost of an extra 360 meters in one�s
daily commute, under di¤erent commuting options. Postulating one round-trip per day, 5 days
per week, this amounts to 225 extra kilometers per year. To compute the time-cost component
of commuting, I estimate hourly wages by dividing the average yearly wage in my sample
(93950 Rs.) by 312 yearly working days and 7 daily working hours, obtaining a �gure of 43
Rs. per hour. Assuming that trips take place on foot, at a speed of 4:5 km per hour, a
one-standard deviation deterioration in shape amounts to 50 extra commute hours per year,
which is equivalent to 2:3% of the yearly wage. This �gure is roughly 45% of the welfare cost
I estimate. Assuming instead that trips occur by car, postulating a speed of 25 km per hour,
a fuel e¢ ciency of 5 liters per 100 km, and fuel prices of 77 Rs. per liter23, the direct cost of
increased commute length amounts to 1:3% of the yearly wage, or roughly one quarter of the
welfare cost estimated above.
To complete the exercise, let us now consider the e¤ect of city shape S on �rms. The signs
of the reduced-form estimates for BW ; BN and BP are in principle compatible with city shape
being a production amenity or disamenity. The e¤ect of S on productivity is pinned down by
23These �gures are based respectively on: Ministry of Urban Development, 2008; U.S. Energy Informa-
tion Administration, 2014; http://www.shell.com/ind/products-services/on-the-road/fuels/fuel-pricing.html ac-
cessed in August 2014.
34
equation (37) from Section 3:
c�A = (1� � � )cBN + (1� )dBWwhere parameters � and represent the shares of labor and tradeable capital in the production
function postulated in equation (7). My most conservative point estimates for cBN anddBW are
�0:0981 and 0:038, from Tables 3C and 5 respectively. Setting � to 0.4 and to 0.3 the impliedc�A is �0:003. which implies a productivity loss of about 0:001 log points for a one standarddeviation deterioration in city disconnection. These estimates appear very small, and sensitive
to the choice of parameter values. Postulating a labor share of 0:5 the implied productivity
e¤ect becomes positive: 0:002 log points for a one-standard deviation deterioration in shape.
This exercise thus yields inconclusive results. Although the currently available evidence seems
to indicate that the cost of disconnected shape is mostly borne by consumers, more work will
be required to understand the implications of city shape for �rms, possibly disaggregating by
sector.
6.5 Channels and Heterogeneous E¤ects
The results presented so far provide evidence that consumers have a preference for more com-
pact cities. In this Section, I seek to shed light on the mechanisms through which city shape
a¤ects consumers, and on the categories of consumers who are a¤ected the most by poor urban
geometry.
Infrastructure
Discussing the role of city shape, the urban planning literature typically emphasizes commute
times as the main argument in favor of more compact city shapes. If transit times are indeed
the main channel through which urban shape matters, road infrastructure should mitigate the
adverse e¤ects of poor geometry. By the same argument, all else being equal, consumers with
individual means of transport should be less a¤ected by city shape.
[Insert Table 7]
In Table 7 I attempt to investigate these issues interacting city shape with a number of
indicators for infrastructure. For ease of interpretation, I resort to the more parsimonious
35
Speci�cation II, which links normalized shape to population density (eq. (46) and (47)). Pop-
ulation density is measured in thousand inhabitants per squared km. Results are reported for
the disconnection and range index. Recall that these two indexes represent respectively the
average and maximum length of within-city trips. While disconnection is a general indicator
for city shape, the range index might be more suitable to capture longer within-city trips, which
might be more likely to require motorized means of transportation.
This exercise is subject to a number of caveats. An obvious identi�cation challenge lies
in the fact that infrastructure is not exogenous, but rather jointly determined with urban
shape. This issue is investigated explicitly in Section 7.2, in which I present some results on
current road infrastructure and city shape. In Table 7 I partly address the endogeneity of city
infrastructure by employing state-level proxies. In columns 1 and 2, instrumented normalized
shape is interacted with state-level motor vehicles density measured in 1991 - the �rst year for
which this statistic was available24. This �gure is provided by the Ministry of Urban Transport
and Highways. In columns 3 and 4, I interact shape with urban road density in 1991, as reported
by the 1991 Census Town Directory; again, 1991 is the �rst year in which the Census provides
this �gure. To cope with the potential endogeneity of this variable, in columns 5 and 6 I employ
instead a state-level, leave-out mean of 1991 urban road density in the state. The coe¢ cients on
all three interaction terms - with the exception of the one in column 5 - are positive and highly
signi�cant, which can be interpreted as evidence that infrastructure mitigates the negative
e¤ects of poor geometry. However, we cannot fully rule out potential confounding e¤ects: for
instance, these positive interaction coe¢ cients might be capturing di¤erential trends across
cities with di¤erent incomes.
.Housing quality
[Insert Table 8 ]
A complementary question relates to who bears the cost of poor city geometry. Emphasizing
the link between city shape, transit and poverty, Bertaud (2004) claims that compact cities are
in principle more favorable to the poor because they reduce distance, particularly in countries
where they cannot a¤ord individual means of transportation or where the large size of the city
24Unfortunately, I cannot compute a leave-out mean because I don�t have access to city-level data on motor
vehicles density.
36
precludes walking as a means of getting to jobs. At the same time, however, if compact cities
are also more expensive, this would tend to reduce the housing �oor space which the poor
can a¤ord (Bertaud, 2004). In Table 8, I make an attempt to investigate the link between
poverty and city shape by looking at two - admittedly very rough - proxies for city income:
the total and the fraction of slum dwellers and a principal component wealth index based
on physical characteristics of houses, including roof, wall and �oor material as well as the
availability of running water and a toilet. This information is provided in the Census for a
limited number of cities and years. As in previous tables, I provide IV estimates obtained with
both Speci�cation I and II, as well as OLS estimates for Speci�cation I. I �nd that cities with
less compact shapes have overall fewer slum dwellers, both in absolute terms and relative to
total population. Moreover, less compact cities are characterized by houses of marginally better
quality. In principle, this could arise from higher equilibrium rents in compact cities, which
could be forcing more people into substandard housing. A more interesting interpretation,
however, is that poorer migrants sort into cities with more compact shapes, possibly because
of their lack of individual means of transport and consequent higher sensitivity to commute
lengths. It is plausible that the marginal migrant to urban India would start out as slum
dweller, which substantiates the sorting hypothesis.
7 Empirical Results: Endogenous Responses to City Shape
The evidence presented so far indicates that city shape a¤ects the spatial equilibrium across
cities, and in particular that deteriorating urban geometry entails welfare losses for consumers.
A natural question which arises next concerns the role of policy: given that most cities can-
not expand radially due to their topographies, what kind of land use regulations, if any, and
infrastructural investments best accommodate city growth? Although a thorough normative
analysis requires more theoretical work and possibly more detailed data than those used in this
study, this section provides some evidence on the interaction between topography, city shape
and policy. Due to data availability constraints, part of the analyses carried out in this section
are based on comparatively small samples and/or rely on cross-sectional variation only. These
results should therefore be interpret cautiously.
FARs
37
I start by considering the most controversial among land use regulations currently in place
in urban India: Floor Area Ratios (FAR). As explained in Section 4.6, FARs are restrictions on
building height expressed in terms of the maximum allowed ratio of a building�s �oor area over
the area of the plot on which it sits. Higher values allow for taller buildings. Previous work has
linked the restrictive FARs in place in Indian cities to suburbanization and sprawl (Sridhar,
2010; Sridhar and Malpezzi, 2012), as measured by administrative data sources. Bertaud and
Brueckner (2005) analyze the welfare impact of FARs in the context of a monocentric city
model, estimating that restrictive FARs in Bengaluru carry a welfare cost ranging between 1.5
and 4.5%.
Information on FAR values across Indian cities is very hard to obtain. My data on FARs is
drawn from Sridhar (2010), who collects a cross-section of the maximum allowed FAR levels as
of the mid-2000s, for about 50 cities25, disaggregating by residential and non-residential FAR.
Based on discussions with urban local bodies and developers, it appears that FARs are very
resilient, and have been rarely updated. While the data collected by Sridhar re�ects FARs as
they were in the mid-2000s, they are likely to be a reasonable proxy for FAR values in place
throughout the sample.
[Insert Table 9]
In Table 9, panel A, I explore the interaction between topography and FARs in determining
city shape and area. The three �rst-stage equations presented in Table 2 are reproposed here,
augmented with an interaction between each instrument and FAR levels. Each observation is a
city-year. In columns 1, 2 and 3 I consider the average of residential and non-residential FARs,
whereas in columns 4, 5 and 6 I focus on residential FARs.
The main coe¢ cients of interest are the interaction terms. The interaction between projected
population and FARs appears to have a negative impact on city area (columns 2 and 4),
indicating that laxer FARs cause cities to expand less in space than their projected growth
would imply. This is in line with the results obtained by Sridhar (2010) who �nds a cross-
sectional correlation between restrictive FARs and sprawl using administrative, as opposed
25Sridhar (2010) collectes data for about 100 cities, but many of those cities are part of larger urban agglom-
erations, and do not have appear as individual footprints in my panel. Moreover, some are too small to be
detected by night-time lights. This reduces the e¤ective number of observations which I can use in my panel to
55. My analysis is thus subject to signi�cant power limitations.
38
to remotely-sensed data. This interaction term has a negative impact on city shape as well
(columns 1 and 5), suggesting that higher FARs also can slow down the deterioration in city
shape which city growth entails. The interaction between potential shape and FARs in column
3 is also negative, indicating that cities with higher FARs have a more compact shape then their
topography would predict. This seems to suggest that if growing and/or potentially constrained
cities are allowed to build vertically, they will do so, rather than expand horizontally and face
topographic obstacles.
In Table 9, panel B, I investigate the impact of FARs interacted with city shape on popu-
lation and density. Again, each observation is a city-year. The speci�cations proposed here are
equivalent to those in Table 3, augmented with interactions between the explanatory variables
and FARs. The corresponding interacted �rst-stage equations are proposed in panel A. Results
are mixed, possibly due to small sample size. However, the results from the interacted version
of Speci�cation II (columns 1 and 4) suggest that laxer FARs mitigate the negative impact
of non-compactness on population: the interaction between instrumented shape and FARs is
positive, and signi�cant in the case of residential FARs. An interpretation for this result is that
long potential commutes matter less in cites which allow taller buildings, since this allows more
consumers to live in central locations. This result, however, is not robust to the alternative
Speci�cation I (columns 2 and 5).
My next question relates to the determinants of FARs, in particular whether urban form
considerations appear to be incorporated by policy makers in setting FARs. Panel C of Table 9
provides an attempt to investigate this issue by regressing FAR values on urban form indicators
- shape and area - as measured in year 2005. The estimating equations are a cross-sectional
versions of eq. (43) and (48), with FARs as a dependent variable. Each observation is a city in
year 2005. Subject to the limitations of cross-sectional inference and small sample size, these
results indicate that larger cities have more restrictive FARs, both in the IV and in the OLS.
This is consistent with one of the stated objectives of FARs: curbing densities in growing cities.
At the same time, however, the coe¢ cient on shape is positive, both in the IV and in the OLS.
This could either indicate a deliberate willingness of policy makers to allow for taller buildings
in areas with constrained topographies, or might re�ect a historical legacy of taller architecture
39
in more constrained cities26.
Road infrastructure
Next, I turn to another type of policy response to city shape: road infrastructure. In Section
6.3 I provide some suggestive evidence that infrastructure might mitigate the adverse e¤ects of
poor shape. In this section I am interested in the complementary question of whether current
road infrastructure responds to city shape, and whether denser road networks are compensating
for longer potential trips in less compact cities. Although the Census provides urban road den-
sity for a subset of cities and years, these data appear to be based on administrative boundaries
which are seldom updated. Instead, I compute the total length of the current road network as
it appears on the maps available on Openstreetmap, overlapping the street network with my
night-time lights-based urban footprint boundaries. More details can be found in Section 4.6.
In Table 10 I investigate the cross-sectional relationship between current road network and city
shape, measured in 2010 - the most recent year in my sample
[Insert Table 10]
Each observation in Table 10 is a city in year 2010. Results are reported for the disconnection
(columns 1 to 3) and range index (column 4 to 6). Recall that these two indexes represent
respectively the average and maximum length of within-city trips. While disconnection is a
general indicator for city shape, the range index might be more suitable to capture cross-
city trips, possibly requiring highways. Panel A considers total road length, whereas panel B
considers road length per capita. Columns 1 and 4 report the IV results from estimating a
cross-sectional version of Speci�cation I (equation (43)). Columns 3 and 6 report the same
speci�cation, estimated by OLS. Columns 2 and 5 report the IV results from estimating a
cross-sectional version of Speci�cation II (equation (46)).
Results are somewhat mixed, and not always consistent across speci�cations. However, the
general pattern discernible from the IV results seems to be the following: non-compact cities
have a road network which is less dense in absolute terms, but road density per person which
is not statistically di¤erent from that of compact cities27 .
26Discussions with urban local bodies and developers suggest that FARs re�ect to some extent the traditional
architectural style of di¤erent cities.27The OLS coe¢ cients display the opposite pattern: more disconnected cities have a denser road network
40
Location of establishments
I conclude by providing some preliminary evidence on another type of endogenous response
to deteriorating shape: a tendency to become less monocentric and more dispersed. It is
conceivable that, as cities grow into larger and more disconnected footprints, resulting in lengthy
commutes to the historic core, businesses might choose to locate further apart from each other,
and/or possibly form new business districts elsewhere. I attempt to shed light on this hypothesis
by analyzing the spatial distribution of productive establishments listed in the Urban Directories
of the 2005 Economic Census This data source is described in greater detail in Section 4.6.
The literature has proposed a number of methodologies to detect employment sub-centers
within cities, mostly based on relative employment densities (Anas et al., 1998). At this stage, I
employ a very simple indicator of concentration: Moran�s I statistic (Anselin, 1995), an index of
spatial clustering which has been proposed as an indicator of monocentricity vis-a-vis dispersion
(Tsai, 2005).
[Insert Table 11]
In Table 11 I estimate the relationship between spatial concentration of �rms, area and
shape, in a cross-section of footprints observed in 2005. The dependent variable is Moran�s I
statistic, computed for the locations of establishments in each footprint. Higher values indicate
greater spatial clustering. Results are reported for the disconnection (columns 1 to 3) and range
index (column 4 to 6). Again, I consider cross-sectional versions of Speci�cations I (eq. 43) and
II (eq. 48) The IV estimates suggest that establishments might be more spread out in cities
with more disconnected shapes. If con�rmed by further analyses, this could indicate a more
pronounced tendency towards dispersion or polycentricity in cities whose shape is deteriorating.
in absolute, but not in per capita terms. This could be generated by the correlation between city size and
non-compactness discussed in Section 6.1. Growing cities are typically less compact, and also tend to have
better infrastructure. The observed pattern can be due to the fact that the spurious correlation between
non-compactness and population is stronger than that between non-compactness and infrastructure - possibly
because in rapidly expanding cities infrastructure responds to population growth with a delay.
41
8 Conclusions
In this project I investigate empirically the economic implications of city shape in the context
of India. My results indicate that city geometry does a¤ect the location choices of consumers,
in the framework of spatial equilibrium across cities. In particular, my �ndings are consistent
with compact city shape being valued as a consumption amenity. I estimate the welfare cost of
deteriorating city shape to be roughly twice as large as the direct implied increase in commute
cost. I also investigate interactions between policy and geography in determining urban shape,
�nding that restrictions on building height - in the form of low FARs - result in cities which
are more spread out in space and less compact.
This project leaves a number of open questions for future research. First, my approach
captures the overall e¤ects of urban geometry, measured at the city level, but does not explicitly
address the implications of geometry for the spatial equilibrium within cities. More work will
be required to develop a theoretical framework and deliver testable implications for how city
shape a¤ects the location choices and commute patterns of consumers within cities. Although
my empirical analysis highlights that more compact cities are generally preferred by the average
consumer, it does not answer the question of who bears the costs of disconnected geometry
within each city, and through which mechanisms. More detailed, geo-referenced data at the
sub-city level might help shed light on these issues.
It would be also important to pin down with more con�dence the channels through which
city shape a¤ects consumers. Throughout this project I interpret city geometry mainly as
a shifter of commuting costs, and I employ shape metrics speci�cally constructed to capture
the implications of shape for transit. Moreover, the evidence provided in section 6.3 seems to
support the interpretation that urban commutes are indeed the main channel through which city
shape a¤ects location choices. However, there could be other, second-order channels through
which city shape might have economically-relevant e¤ects. First, as noted by Bertaud (2002),
geometry a¤ects not only transportation but all kinds of urban utilities delivered through
spatial networks, including those collecting and distributing electricity, water and sewerage.
The optimal layout of such networks is founded on di¤erent engineering theories than those
which found transport, and di¤erent shape indicators would be required to capture these aspects
of shape. However, there might still be interactions with the shape metrics used in my analysis.
Second, the same topographic obstacles which make cities "disconnected" from an urban transit
42
perspective, might also act as boundaries, promoting the separation of a city in di¤erent,
disconnected neighborhoods and/or administrative units. This could have implications both
in terms of political economy and of segregation. Previous research, although in very di¤erent
contexts, suggests this might be the case: for instance, Hoxby (2000) �nds that the number of
school districts in US cities is predicted by the number of natural barriers. Ananat (2011) �nds
that US cities which were subdivided by railroads into a larger number of physically de�ned
neighborhoods became more segregated. Similarly, disconnected urban footprints might provide
a "technology" for creating segregation. Again, more disaggregated data at the sub-city level
will be required to investigate these rami�cations.
Finally, more work is required to understand the response of �rms to city shape. City shape
has the potential to a¤ect �rms both directly, by increasing transportation costs,and indirectly,
by distorting their location choices. In Section 8 I provide some preliminary evidence that
�rms tend to be more spread out in disconnected cities. This might re�ect an attempt to
counteract the spatial mismatch with potential employees, but could come at the expenses of
agglomeration externalities. These e¤ects are likely to be heterogeneous across sectors, which
would raise the complementary question of whether �rms in di¤erent sectors sort into cities
with di¤erent geometries.
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46
Table 1: Descriptive Statistics
Obs. Mean St.Dev. Min Max
Area, km2
6276 62.63 173.45 0.26 3986.02
Remoteness, km 6276 2.42 2.22 0.20 27.43
Spin, km2
6276 12.83 39.79 0.05 930.23
Disconnection, km 6276 3.30 3.05 0.27 38.21
Range, km 6276 9.38 9.11 0.86 121.12
Norm. remoteness 6276 0.71 0.06 0.67 2.10
Norm. spin 6276 0.59 0.18 0.50 6.81
Norm. shape 6276 0.97 0.08 0.91 2.42
Norm. range 6276 2.74 0.35 2.16 7.17
City population 1440 422869 1434022 5822 22085130
City population density (per km2) 1440 15011 19124 432 239179
Avg. yearly wage, thousand 2014 Rs. 2009 93.95 66.44 13.04 838.55
Avg. yearly rent per m2, 2014 Rs. 895 603.27 324.81 104.52 3821.59
47
(1) (2) (3)
OLS OLS OLS
Shape of actual
footprint, km
Log area of actual
footprint, km2
Norm. shape of actual
footprint
Shape of potential footprint, km 0.352*** 0.0562***
(0.0924) (0.0191)
Log projected historic population 0.390** 0.488***
(0.160) (0.102)
Norm. shape of potential footprint 0.0413***
(0.0141)
Observations 6,276 6,276 6,276
Shape of potential footprint, km 0.585*** -7.43e-05
(0.213) (0.000760)
Log projected historic population 2.470 0.571***
(2.456) (0.101)
Norm. shape of potential footprint 0.0249**
(0.0103)
Observations 6,276 6,276 6,276
Shape of potential footprint, km 1.392*** 0.152***
(0.229) (0.0457)
Log projected historic population -1.180*** 0.307***
(0.271) (0.117)
Norm. shape of potential footprint 0.0663***
(0.0241)
Observations 6,276 6,276 6,276
Shape of potential footprint, km 1.935*** 0.0641***
(0.357) (0.0212)
Log projected historic population -4.199*** 0.310***
(0.977) (0.117)
Norm. shape of potential footprint 0.0754**
(0.0344)
Observations 6,276 6,276 6,276
Model for city-specific city-specific common rate
City FE YES YES YES
Year FE YES YES YES
Table 2: First Stage
Notes: this table reports estimates of the first-stage relationship between city shape and area, and the instruments discussed in Section 5.1. Each observation is a
city-year. Columns (1), (2), (3) report the results from estimating respectively equations (44), (45), (47). The dependent variables are shape, in km, log area, in
km2, and normalized shape (dimensionless) of the actual city footprint. The corresponding instruments are shape of the potential footprint, in km, log projected
historic population and normalized shape of the potential footprint. The construction of the potential footprint is based on a city-specific model for city expansion in
columns (1) and (2), and on a common rate one in column (3) - see Section 5.1. Shape is measured by different indexes in different panels. Remoteness (panel A)
is the average length of trips to the centroid. Spin (panel B) is the average squared length of trips to the centroid. Disconnection (panel C) is the average length of
within-city trips. Range (panel D) is the maximum length of within-city trips. City shape and area are calculated from maps constructed from the DMSP/OLS Night-
time Lights dataset (1992-2010) and U.S. Army maps (1951). Estimation is by OLS. All specifications include city and year fixed effects. Standard errors are
clustered at the city level.*** p<0.01,** p<0.05,* p<0.1.
A. Shape Metric: Remoteness
B. Shape Metric: Spin
C. Shape Metric: Disconnection
D. Shape Metric: Range
48
(1) (2) (3)
IV IV OLS
Log population Population density Log population
Shape of actual footprint, km -0.137** 0.0338***
(0.0550) (0.0112)
Log area of actual footprint, km2
0.785*** 0.167***
(0.182) (0.0318)
Norm. shape of actual footprint -311.8***
(92.18)
Observations 1,440 1,440 1,440
Shape of actual footprint, km -0.00101 0.000887***
(0.000657) (0.000288)
Log area of actual footprint, km2
0.547*** 0.197***
(0.101) (0.0290)
Norm. shape of actual footprint -110.9***
(37.62)
Observations 1,440 1,440 1,440
Shape of actual footprint, km -0.0991** 0.0249***
(0.0386) (0.00817)
Log area of actual footprint, km2
0.782*** 0.167***
(0.176) (0.0318)
Norm. shape of actual footprint -254.6***
(80.01)
Observations 1,440 1,440 1,440
Shape of actual footprint, km -0.0284*** 0.00763***
(0.0110) (0.00236)
Log area of actual footprint, km2
0.746*** 0.171***
(0.164) (0.0305)
Norm. shape of actual footprint -84.14***
(27.70)
Observations 1,440 1,440 1,440
Model for city-specific common rate
City FE YES YES YES
Year FE YES YES YES
Table 3: Impact of City Shape on Population
A. Shape Metric: Remoteness
B. Shape Metric: Spin
C. Shape Metric: Disconnection
D. Shape Metric: Range
Notes: this table reports estimates of the relationship between city shape and population. Each observation is a city-year. Column (1) reports the results from estimating
equation (43) (Specification I). The dependent variable is log city population. The explanatory variables are log city area, in km2, and city shape, in km. Column (2) reports
the results from estimating equation (46) (Specification II). The dependent variable is population density, in thousands of inhabitants per km2. The explanatory variable is
normalized shape (dimensionless). In columns (1) and (2) estimation is by IV. The instruments are discussed in Section 5.2, and the corresponding first-stage estimates are
reported in Table 2. The construction of the potential footprint is based on a city-specific model for city expansion in columns (1) and (2), and on a common rate one in
column (3) - see Section 5.1. Column (3) reports the same specification as column (1), estimated by OLS. Shape is measured by different indexes in different panels.
Remoteness (panel A) is the average length of trips to the centroid. Spin (panel B) is the average squared length of trips to the centroid. Disconnection (panel C) is the
average length of within-city trips. Range (panel D) is the maximum length of within-city trips. City shape and area are calculated from maps constructed from the
DMSP/OLS Night-time Lights dataset (1992-2010) and U.S. Army maps (1951). Population is drawn from the Census of India (1951, 1991, 2001, 2011). All specifications
include city and year fixed effects. Standard errors are clustered at the city level.*** p<0.01,** p<0.05,* p<0.1.
49
(1) (2) (3) (4) (5) (6)
FS(1) FS(2) IV FS(1) FS(2) IV
Shape of actual
footprint, km
Log area of actual
footprint, km2
Log population Shape of actual
footprint, km
Log area of actual
footprint, km2
Log population
Shape of potential
footprint, km 1.365*** 0.155*** 1.376*** 0.158***
(0.228) (0.0462) (0.233) (0.0488)
Log projected historic
population -1.201*** 0.278** -1.213*** 0.294**
(0.267) (0.118) (0.276) (0.123)
Shape of actual
footprint, km -0.100** -0.109**
(0.0414) (0.0428)
Log area of actual
footprint, km2
0.776*** 0.796***
(0.190) (0.185)
Observations 6,006 6,006 1,373 5,996 5,996 1,385
Cities 433 433 433 440 440 440
Sample excludes coastal cities coastal cities coastal cities mountainous cities mountainous cities mountainous cities
City FE YES YES YES YES YES YES
Year FE YES YES YES YES YES YES
Notes: this table presents a robustness check to Tables 2 and 3, excluding cities with “extreme” topographies from the sample. Each observation is a city-year. Columns (1), (2) and (4), (5) are equivalent to columns (1), (2)
in Table 1. They report OLS estimates of the first-stage relationship between city shape and area and the instruments discussed in Section 5.1. Columns (3) and (6) are equivalent to column (1) in Table 3, and report IV
estimates of the impact of shape on log city population. Shape is captured by the disconnection index, which measures the average length of trips within the city footprint, in km. The construction of the potential footprint is
based on a city-specific model for city expansion – see Section 5.1. Columns (1) to (3) exclude from the sample cities located within 5 km from the coast. Columns (4) to (6) exclude from the sample cities with an elevation
above 600 m. City shape and area are calculated from maps constructed from the DMSP/OLS Night-time Lights dataset (1992-2010) and U.S. Army maps (1951). Population is drawn from the Census of India (1951, 1991,
2001, 2011). Elevation is from the ASTER dataset. All specifications include city and year fixed effects. Standard errors are clustered at the city level. *** p<0.01,** p<0.05,* p<0.1.
Table 4: First Stage and Impact of City Shape on Population, Robustness to Excluding Cities with Extreme Topographies
50
(1) (2) (3) (4) (5) (6) (7) (8) (9)
IV IV OLS IV IV OLS IV IV OLS
Shape of actual
footprint, km 0.0381 0.109*** 0.0538*** 0.0626 0.0996*** 0.0586*** 0.0600* 0.112*** 0.0512***
(0.0386) (0.0275) (0.0172) (0.0536) (0.0336) (0.0150) (0.0360) (0.0300) (0.0181)
Log area of actual
footprint, km2 -0.409 -0.0478 -0.167 -0.00936 -0.337 -0.0308
(0.390) (0.0356) (0.465) (0.0516) (0.392) (0.0478)
Observations 2,009 2,009 2,009 1,075 1,075 1,075 1,517 1,517 1,517
Model for city-specific common rate city-specific common rate city-specific common rate
City FE YES YES YES YES YES YES YES YES YES
Year FE YES YES YES YES YES YES YES YES YES
Table 5: Impact of City Shape on Wages
Notes: this table reports estimates of relationship between city shape and average wages. Each observation is a city-year. The dependent variable is the log urban average of individual yearly wages in the city’s district, in thousand 2014
Rupees. The explanatory variables are log city area, in km2, and city shape, in km. Columns (1), (4), (7) report the results from estimating equation (43) (Specification I) by IV. Columns (3), (6), (9) report the same specification, estimated
by OLS. Columns (2), (5), (8) report the results from estimating equation (48) (Specification II) by IV. Instruments are described in Section 5.2. The construction of the potential footprint is based on a city-specific model for city expansion
in columns (1), (4) and (7), and on a common rate one in column (2), (5), (8) – see Section 5.1. In columns (4), (5), (6) the sample is restricted to districts containing only one city. In columns (7), (8), (9) the sample is restricted to cities
which are either the only ones or the top ones in their respective districts. Shape is captured by the disconnection index, which measures the average length of trips within the city footprint, in km. City shape and area are calculated from
maps constructed from the DMSP/OLS Night-time Lights dataset (1992-2010). Wages are from the Annual Survey of Industries, waves 1990, 1994, 1995, 1997, 1998, 2009, 2010. All specifications include city and year fixed effects.
Standard errors are clustered at the city level. *** p<0.01,** p<0.05,* p<0.1.
Dependent variable: log wage
All districts Only districts with one city Only top city per district
51
(1) (2) (3) (4) (5) (6) (7) (8) (9)
IV IV OLS IV IV OLS IV IV OLS
Shape of actual
footprint, km-0.596 -0.303 0.00204 -0.518* -0.636 -0.00857 -0.684 -0.198 0.0107
(0.396) (0.758) (0.0505) (0.285) (1.661) (0.0736) (0.538) (0.806) (0.0516)
Log area of actual
footprint, km2 -1.529 -0.0176 -0.919 -0.0632 -1.407 -0.0355
(1.409) (0.0847) (0.870) (0.108) (1.582) (0.0962)
Observations 895 895 895 476 476 476 711 711 711
Shape of actual
footprint, km-0.675 -0.274 -0.00526 -0.594* -0.595 -0.00736 -0.790 -0.143 0.00685
(0.432) (0.752) (0.0577) (0.324) (1.626) (0.0825) (0.604) (0.780) (0.0590)
Log area of actual
footprint, km2 -1.649 -0.00333 -1.040 -0.0485 -1.586 -0.0141
(1.542) (0.0976) (0.990) (0.125) (1.786) (0.110)
Observations 895 895 895 476 476 476 711 711 711
Model for city-specific common rate city-specific common rate city-specific common rate
City FE YES YES YES YES YES YES YES YES YES
Year FE YES YES YES YES YES YES YES YES YES
Notes: this table reports estimates of relationship between city shape and average housing rents. Each observation is a city-year. In panel A the dependent variable is the log urban average of housing rent per m2
in the city’s district, in
2014 Rupees. In panel B the dependent variable is analogous, but the average is calculated considering only the top 50% of the district’s distribution of rents per m2. The explanatory variables are log city area, in km2, and city shape, in
km. Columns (1), (4), (7) report the results from estimating equation (43) (Specification I) by IV. Columns (3), (6), (9) report the same specification, estimated by OLS. Columns (2), (5), (8) report the results from estimating equation (48)
(Specification II) by IV. Instruments are described in Section 5.2. The construction of the potential footprint is based on a city-specific model for city expansion in columns (1), (4) and (7), and on a common rate one in column (2), (5), (8)
– see Section 5.1. In columns (4), (5), (6) the sample is restricted to districts containing only one city. In columns (7), (8), (9) the sample is restricted to cities which are either the only ones or the top ones in their respective districts.
Shape is captured by the disconnection index, which measures the average length of trips within the city footprint, in km. City shape and area are calculated from maps constructed from the DMSP/OLS Night-time Lights dataset (1992-
2010). Housing rents are from the NSS Household Consumer Expenditure Survey, rounds 62 (2005-2006), 63 (2006-2007) and 64 (2007-2008). All specifications include city and year fixed effects. Standard errors are clustered at the
city level. *** p<0.01,** p<0.05,* p<0.1.
B. Dependent variable: log yearly rent per square meter, upper 50%
Table 6: Impact of City Shape on Housing Rents
All districts Only districts with one city Only top city per district
A. Dependent variable: log yearly rent per square meter
52
(1) (2) (3) (4) (5) (6)
IV IV IV IV IV IV
Norm. shape -183.9*** -48.25*** -103.9*** -30.34*** -140.5*** -37.71***
(39.53) (9.047) (18.10) (5.485) (44.85) (9.934)
Norm. shape x
state motor vehicles density, 1991 0.0462*** 0.0246***
(0.0179) (0.00441)
Norm. shape x
urban road density, 1991 0.204*** 0.0692***
(0.0204) (0.00776)
Norm. shape x
state urban road density, 1991 0.000462 0.000207*
(0.000312) (0.000107)
Observations 1,286 1,286 1,406 1,406 1,380 1,380
Shape metric disconnection range disconnection range disconnection range
City FE YES YES YES YES YES YES
Year FE YES YES YES YES YES YES
Notes: this table investigates the impact of shape, interacted with infrastructure, on population. Each observation is a city-year. All columns report IV estimates of a specification similar to equation (46) (Specification II),
augmented with an interaction between normalized shape and different infrastructure proxies. The dependent variable is population density, in thousands of inhabitants per km2. The construction of the potential footprint is
based on a city-specific model for city expansion – see Section 5.1. The shape metrics considered are the normalized disconnection index (columns (1), (3), (5)), and normalized range index (columns (2), (4), (6)).
Disconnection is the average length of within-city trips. Range is the maximum length of within-city trips. In columns (1), (2) normalized shape is interacted with state motor vehicles density in 1991 (source: Ministry of Road
Transport and Highways). In columns (3), (4) normalized shape is interacted with urban road density in the city, as reported in the 1991 Census. In columns (4), (5) normalized shape is interacted with a leave-out mean of
urban road density in the state calculated using 1991 Census data and data from the Ministry of Road Transport and Highways .City shape and area are calculated from maps constructed from the DMSP/OLS Night-time
Lights dataset (1992-2010) and U.S. Army maps (1951). Population is drawn from the Census of India (1951, 1991, 2001, 2011). All specifications include city and year fixed effects. Standard errors are clustered at the city
level. *** p<0.01,** p<0.05,* p<0.1.
Table 7: Interactions of City Shape with Infrastructure
Dependent variable: population density
53
(1) (2) (3) (4) (5) (6) (7) (8) (9)
IV IV OLS IV IV OLS IV IV OLS
Shape of actual
footprint, km -0.134** -0.0431 -0.0353** -0.113** -0.0501*** -0.0498*** 0.195* 0.174* -0.00698
(0.0540) (0.0437) (0.0167) (0.0561) (0.0185) (0.0169) (0.118) (0.0940) (0.0312)
Log area of actual
footprint, km2
0.592 0.134 0.264 0.0501 0.438 0.141
(0.492) (0.0829) (0.633) (0.0938) (1.483) (0.120)
Observations 1,067 1,067 1,067 1,067 1,067 1,067 822 822 822
Model for city-specific common rate city-specific common rate city-specific common rate
City FE YES YES YES YES YES YES YES YES YES
Year FE YES YES YES YES YES YES YES YES YES
Table 8: Impact of City Shape on Housing Quality
Notes: this table reports estimates of relationship between city shape and proxies for housing quality. Each observation is a city-year. Columns (1), (4), (7) report the results from estimating equation (43) (Specification I) by IV.
Columns (3), (6), (9) report the same specification, estimated by OLS. Columns (2), (5), (8) report the results from estimating equation (48) (Specification II) by IV. The explanatory variables are shape, in km, and log city area, in
km2. Instruments are described in Section 5.2. The construction of the potential footprint is based on a city-specific model for city expansion in columns (1), (4) and (7), and on a common rate one in column (2), (5), (8) – see
Section 5.1. The dependent variables are the following: log slum population in the city (columns (1), (2), (3)), log of the share of slum to total population in the city (columns (4), (5), (6)), and a housing quality principal component
index (columns (7), (8), (9)). Data on slums are drawn from the 1991, 2001 and 2011 Census. The housing quality index is the city-year average of a principal component index based on the following characteristics of Census
houses: roof, wall and floor material, availability of running water and toilet in-premise. The source is the 2001 and 2011 Census. Shape is captured by the disconnection index, which measures the average length of trips within
the city footprint, in km. City shape and area are calculated from maps constructed from the DMSP/OLS Night-time Lights dataset (1992-2010). All specifications include city and year fixed effects. Standard errors are clustered at
the city level. *** p<0.01,** p<0.05,* p<0.1.
Log slum population shareLog slum population Housing index
54
(1) (2) (3) (4) (5) (6)
OLS OLS OLS OLS OLS OLS
Shape
of actual
footprint, km
Log area
of actual
footprint, km2
Norm. shape
of actual
footprint
Shape
of actual
footprint, km
Log area
of actual
footprint, km2
Norm. shape
of actual
footprint
Log projected historic population 2.998 1.984** 1.322 1.086*
(2.758) (0.795) (1.841) (0.647)
-1.958* -0.686** -1.315* -0.342
(1.023) (0.319) (0.779) (0.270)
Shape of potential footprint, km 0.156 -0.186 0.235 0.0928
(1.182) (0.233) -0.671 (0.187)
0.665 0.135 0.617** 0.0244
(0.487) (0.106) (0.279) (0.0810)
Norm. shape of potential footprint 0.435*** 0.337***
(0.123) (0.117)
-0.0908** -0.0571
(0.0452) (0.0371)
Observations 1,183 1,183 1,183 1,183 1,183 1,183
Model for city-specific city-specific common rate city-specific city-specific common rate
IV IV OLS IV IV OLS
Log populationPopulation
DensityLog population Log population
Population
DensityLog population
Shape of actual footprint, km -0.0979 0.0509 -0.271** 0.0283
(0.124) (0.0312) (0.122) (0.0285)
0.00290 -0.0160 0.0688* -0.00767
(0.0472) (0.0129) (0.0371) (0.0103)
Log area of actual footprint, km2
0.683** 0.0109 0.828*** -0.0443
(0.338) (0.128) (0.308) (0.103)
0.0995 0.0665 0.00166 0.0981***
(0.116) (0.0471) (0.0886) (0.0368)
Norm. shape of actual footprint -97.49 -85.46
(102.5) (108.1)
-10.91 -16.89
(43.88) (45.12)
Observations 252 252 252 252 252 252
Model for city-specific common rate city-specific common rate
FAR average average average residential residential residential
City FE YES YES YES YES YES YES
Year FE YES YES YES YES YES YES
Norm. shape of actual footprint
x FAR
Notes: each observation is a city-year. Panel A of this table reports estimates of the first-stage relationship between Floor Area Ratios, city area and shape. Columns (1), (2) (3)
and (4), (5), (6) report the same specifications reported in Table 2, with the addition of interactions between each instrument and FARs. Panel B reports estimates of the
relationship between Floor Area Ratios, shape and population. Columns (1), (2) (3) and (4), (5), (6) report the same specifications reported in Table 3, with the addition of
interactions between each explanatory variable and FARs. FARs are drawn from Sridhar (2010) and correspond to the maximum allowed Floor Area Ratios in each city as of the
mid-2000s. FARs are expressed as ratios of the total floor area of a building over the area of the plot on which it sits. Columns (1), (2), (3) consider the average of residential and
non-residential FARs, while columns (4), (5), (6) only consider residential FARs. Shape is captured by the disconnection index, which measures the average length of trips within
the city footprint, in km. City shape and area are calculated from maps constructed from the DMSP/OLS Night-time Lights dataset (1992-2010) and U.S. Army maps (1951).
Population is from the Census (1951, 1991, 2001, 2011). Population density is measured in thousands of inhabitants per km2. All specifications include city and year fixed effects.
Standard errors are clustered at the city level. *** p<0.01,** p<0.05,* p<0.1.
Table 9: Urban Form and Floor Area Ratios
B. Impact of city shape and FARs on population
A. First-stage impact of FARs on city shape
Shape of potential footprint, km
x FAR
Log projected historic population
x FAR
Norm. shape of potential footprint
x FAR
Shape of actual footprint, km
x FAR
Log area of actual footprint, km2
x FAR
55
(1) (2) (3) (4) (5) (6)
IV IV OLS IV IV OLS
Shape of actual footprint, km 0.0508 0.000290 0.021 0.0715* 0.00515 0.0439**
(0.0409) (0.00741) (0.0140) (0.0401) (0.00914) (0.0199)
Log area of actual footprint, km2
-0.190 -0.105* -0.280 -0.177**
(0.179) (0.0540) (0.176) (0.0876)
Observations 55 55 55 55 55 55
Model for city-specific common rate city-specific common rate
Notes: This table investigates the cross-sectional relationship between city area, shape and Floor Are Ratios as of year 2005. Each observation is a city in year 2005. Columns (1)
and (4) estimate a cross-sectional version of equation (43) (Specification I), with log FARs as a dependent variable, estimated by IV. Columns (3) and (6) present the same
specification, estimated by OLS. Columns (2) and (5) estimate a cross-sectional version of equation (48) (Specification II), with log FARs as a dependent variable, estimated by IV.
FARs are drawn from Sridhar (2010) and correspond to the maximum allowed Floor Area Ratios in each city as of the mid-2000s. FARs are expressed as ratios of the total floor
area of a building over the area of the plot on which it sits. Columns (1), (2), (3) consider the average of residential and non-residential FARs, while columns (4), (5), (6) only
consider residential FARs. Shape is captured by the disconnection index, which measures the average length of trips within the city footprint, in km. City shape and area are
calculated from maps constructed from the DMSP/OLS Night-time Lights dataset, in year 2005. Standard errors are clustered at the city level. *** p<0.01,** p<0.05,* p<0.1.
Avg. FAR Residential FAR
Table 9 (continued): Urban Form and Floor Area Ratios
C. FARs Determinants, 2005
56
(1) (2) (3) (4) (5) (6)
IV IV OLS IV IV OLS
Log road length, km Road density, km/km2 Log road length, km Log road length, km Road density, km/km
2 Log road length, km
Shape of actual footprint, km -0.0769* 0.0231** -0.0237** 0.00655**
(0.0429) (0.0111) (0.0109) (0.00320)
Log area of actual footprint, km2
1.292*** 0.861*** 1.279*** 0.871***
(0.147) (0.0415) (0.115) (0.0379)
Norm. shape of actual footprint 9.131 -3.563
(16.44) (3.816)
Observations 429 429 429 429 429 429
Log road length
per capita
Road density
per capita
Log road length
per capita
Log road length
per capita
Road density
per capita
Log road length
per capita
Shape of actual footprint, km 0.0403 -0.0677*** 0.00753 -0.0190***
(0.0467) (0.0149) (0.0111) (0.00427)
Log area of actual footprint, km2
-0.201 0.346*** -0.143 0.317***
(0.178) (0.0597) (0.138) (0.0547)
Norm. shape of actual footprint -0.0377 -0.0152
(0.0785) (0.0211)
Observations 429 429 429 429 429 429
Model for city-specific common rate city-specific common rate
Shape metric disconnection disconnection disconnection range range range
Notes: This table estimates the cross-sectional relationship between city area, shape and road network as of year 2010. Panel A considers total road length and panel B considers road length per capita. Each observation is a city in year
2010. Columns (1) and (4) estimate a cross-sectional version of equation (43) (Specification I), estimated by IV. Columns (3) and (6) present the same specification, estimated by OLS. In columns (1), (3), (4), (6), panel A, the dependent
variable is log road length in the footprint, in km. In columns (1), (3), (4), (6), panel B, the dependent variable is log road length per capita in the footprint, in km per thousand inhabitants. Columns (2) and (5) estimate a cross-sectional
version of equation (46) (Specification II), estimated by IV. In columns (2), (5), panel A, the dependent variable is road density in the footprint, in km per km2. In columns (2), (5) panel B, the dependent variable is road density per capita,
in in km per km2
per thousand inhabitants. The construction of the potential footprint is based on a city-specific model for city expansion in columns (1) and (4), and on a common rate on in columns (2) and (5) – see Section 5.1. Road
length is computed based on current (2014) Openstreetmap maps of Indian cities, focusing on roads denoted as “trunk”, “primary” or “secondary”. Disconnection is the average length of trips within the city footprint, in km. Range is the
longest possible within-footprint trip, in km. City shape and area are calculated from maps constructed from the DMSP/OLS Night-time Lights dataset, in year 2010. Standard errors are clustered at the city level. *** p<0.01,** p<0.05,*
p<0.1.
A. Total Roads
B. Roads per capita
Table 10: Impact of City Shape on Road Network, 2010
57
(1) (2) (3) (4) (5) (6)
IV IV OLS IV IV OLS
Shape of actual footprint, km -0.198** -0.00633 -0.0410** -0.000758
(0.0978) (0.0248) (0.0182) (0.00673)
Log area of actual footprint, km2
0.395** 0.0519 0.244** 0.0449
(0.181) (0.0498) (0.0958) (0.0403)
Norm. shape of actual footprint 22.33 -1.117
(103.1) (1.345)
Observations 196 196 196 196 196 196
Model for city-specific common rate city-specific common rate
Shape metric disconnection disconnection disconnection range range range
Dependent variable: Moran's I index of spatial concentration
Table 11: Impact of City Shape on the Spatial Distribution of Productive Establishments, 2005
Notes: This table investigates the cross-sectional relationship between city area, shape and the spatial concentration of productive establishments in cities as of year 2005. Each observation is a
city in year 2005. The dependent variable is the Moran’s I index of spatial concentration, computed in each city for the location of productive establishments, as reported in the urban directories of
the 2005 Economic Census. Higher values indicate more spatial clustering. Columns (1) and (4) estimate a cross-sectional version of equation (43) (Specification I), estimated by IV. Columns (3)
and (6) present the same specification, estimated by OLS. Columns (2) and (5) estimate a cross-sectional version of equation (48) (Specification II), estimated by IV. The construction of the
potential footprint is based on a city-specific model for city expansion in columns (1) and (3), and on a common rate on in columns (2) and (4) – see Section 5.1. The shape metrics considered are
the disconnection index (columns (1), (2), (3)), and range index (columns (4), (5), (6)). Disconnection is the average length of trips within the city footprint, in km. Range is the longest possible
within-footprint trip, in km. City shape and area is calculated from maps constructed from the DMSP/OLS Night-time Lights dataset, in year 2005. Standard errors are clustered at the city level. ***
p<0.01,** p<0.05,* p<0.1
58
(1) (2)
IV IV
Log population Population density
Shape of actual footprint, km -0.194***
(0.0596)
Log area of actual footprint, km2
0.973***
(0.222)
Norm. shape of actual footprint -254.6***
(80.01)
Observations 1,440 1,440
Model for city-specific common rate
City FE YES YES
Year FE YES YES
Initial shape x year FE YES YES
Appendix Table 1: Impact of Shape on Population, Robustness to Initial Shape x Year Fixed Effects
Notes: this table presents a robustness check to Table 3, augmenting the specification with year fixed effects interacted with initial shape. Each
observation is a city-year. Columns (1) and (2) are equivalent to columns (1) and (2) in Table 3. They report IV estimates of the relationship between
city shape and area and log city population (col. 1) and population density, in thousand inhabitants per km2
(col.2). Shape is captured by the
disconnection index, which measures the average length of trips within the city footprint, in km. The construction of the potential footprint is based
on a city-specific model for city expansion in column (1) and on a common rate on in column (2) – see Section 5.1. City shape and area are
calculated from maps constructed from the DMSP/OLS Night-time Lights dataset (1992-2010) and U.S. Army maps (1951). Population is drawn
from the Census of India (1951, 1991, 2001, 2011). All specifications include city and year fixed effects, as well as year fixed effects interacted with
the city’s disconnection index measured in the initial year of the panel (1951). Standard errors are clustered at the city level. *** p<0.01,** p<0.05,*
p<0.1.
59
(1) (2) (3) (4) (5) (6)
IV IV IV IV IV IV
Shape of actual footprint, km 0.0116 0.0989*** 0.0393 0.108** 0.0381 0.102***
(0.0420) (0.0272) (0.0768) (0.0421) (0.0386) (0.0298)
Log area of actual footprint, km2 -0.358 -0.164 -0.274
(0.395) (0.465) (0.379)
Observations 2,009 2,009 1,075 1,075 1,517 1,517
Shape of actual footprint, km -0.739 -0.393* -0.670* -0.465* -0.839 -0.447*
(0.487) (0.221) (0.359) (0.265) (0.664) (0.251)
Log area of actual footprint, km2 -1.301 -0.619 -1.092
(1.355) (0.807) (1.444)
Observations 896 896 477 477 712 712
City FE YES YES YES YES YES YES
Year FE YES YES YES YES YES YES
Initial shape x year FE YES YES YES YES YES YES
Model for city-specific common rate city-specific common rate city-specific common rate
Appendix Table 2: Impact of Shape on Wages and Rents, Robustness to Initial Shape x Year Fixed Effects
All districts Only districts with one city Only top city per district
A. Dependent variable: log wage
Notes: this table presents a robustness check to Tables 5 and 6, augmenting the specifications with year fixed effects interacted with initial shape. Each observation is a city-year. In panel A the
dependent variable is the log urban average of individual yearly wages in the city’s district, in thousand 2014 Rupees. In panel B the dependent variable is the log urban average of housing rent
per m2
in the city’s district, in 2014 Rupees. Columns (1), (3), (5) report the results from estimating equation (43) (Specification I) by IV. Columns (2), (4), (6) report the results from estimating
equation (48) (Specification II) by IV. Instruments are described in Section 5.2. The construction of the potential footprint is based on a city-specific model for city expansion in columns (1), (3),
(5), and on a common rate one in column (2), (4), (6) – see Section 5.1. In columns (3), (4) the sample is restricted to districts containing only one city. In columns (5), (6) the sample is
restricted to cities which are either the only ones or the top ones in their respective districts. Shape is captured by the disconnection index, which measures the average length of trips within the
city footprint, in km. City shape and area are calculated from maps constructed from the DMSP/OLS Night-time Lights dataset (1992-2010). Wages are from the Annual Survey of Industries,
waves 1990, 1994, 1995, 1997, 1998, 2009, 2010. Housing rents are from the NSS Household Consumer Expenditure Survey, rounds 62 (2005-2006), 63 (2006-2007) and 64 (2007-2008). All
specifications include city and year fixed effects, as well as year fixed effects interacted with the city’s disconnection index measured in the initial year of the panel (1951). Standard errors are
clustered at the city level. *** p<0.01,** p<0.05,* p<0.1.
B. Dependent variable: log yearly rent per square meter
60
Figure 4
Shape metrics: an example
64
Kolkata
Bengaluru
Shape metric Normalized
Normalized
remoteness, km
14.8 0.99
10.3 0.69
spin, km2
288.4 1.29
120.9 0.54
disconnection, km
20.2 1.35
14 0.94
range, km
62.5 4.18
36.6 2.45